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Computer aided design and computer and computer aided manufacture past question for the year 2020 examines 500-level Engineering students of FUTO, offering MEE505 course on their knowledge of Computer aided design, computer aided manufacture, Isometric view drawing, CNC Codes, rapid traverse positioning, CNC turning, computer aided manufacturing operation, tool-holding magazine, machining centers, milling centers, surface finishing operation, Mathematical matrix notation, Bezier cubic curve, Hermite cubic curve, translation transformation, scaling transformation, rotation transformation, parametric modeling, parametric Bezier equations

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Past Questions related to Computer aided design and computer and computer aided manufacture

Manufacturing process 3

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: IPE507

Topics: Manufacturing process, ultrasonic machining, unconventional machining methods, machined surface accuracy, electrochemical machining, powder metallurgy, gear machining, manufacturing gears, electron beam machining, electro discharge machining

MACHINE DRAWING

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE305

Topics: First Angle Projection, Third Angle Projection, Isometric drawing, Machine Symbols, Surface Texture, Solid Modelling, CAD Software, machine drawing, computer aided design

Engineering Drawing 1

Year: 2020

School: Air Force Institute of Technology

Department: Engineering

Course Code: GET203

Topics: Engineering Drawing, Springs, Crank Mechanism, Isometric Drawing, Orthographic drawing, Screw threads, isometric projection

Engineering drawing 3

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: ENG203

Topics: Engineering drawing, isometric drawing, angle projection, AUTOCAD, instrumental drawing

Mechanical engineering design

Year: 2018

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MCE301

Topics: Mechanical engineering design, design concept, computer-aided design, computer-aided engineering, shaft, gear drive

MANUFACTURING PROCESSES 1-2015,2016,2017,2018,2019

Year: 2019

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE303

Topics: lathe, headstock, tailstock, milling, shaping machine, screw thread, turret lathe, threading, knurling, indexing, turning, machine tools

Machine tools analysis and cutting tool design

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: IPE405

Topics: Machine tools analysis, cutting tool design, Engine lathe, machine tool, machine tool analysis, machine tools, revolution per minute, machining operation, lathe machine accessories, cutting tools nomenclature, milling machine

Engineering Drawing 2

Year: 2021

School: Air Force Institute of Technology

Department: Engineering

Course Code: GET222

Topics: Engineering Drawing, Isometric drawing, Tangency, Cams, Gear, Development of surface

Engineering mathematics 2

Year: 2022

School: University of Ilorin

Department: Engineering

Course Code: CHE264

Topics: Limits, Continuity, differentiation, linear first order differential equations, partial and total derivatives of composite functions, vector algebra, Vector calculus, Directional derivatives, Cauchy-Riemann equations, initial value problems, magnification, rotation, harmonic functions, ordinary differential equations, Wronskian, harmonic function, Laurent series, Green's theorem

Cereal and milling technology

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: FST505

Topics: Cereal technology, milling technology, cereal, conditioning temperng, flour production, patent flour, particle size analysis, maize milling, maize grits, sorghum malt production, instant yam flour production, traditional yam flour production, garri production

Manufacturing process

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE303

Topics: Centre Lathe Machine, Turret Lathe Machine, Shaping Machine, Milling Machine, Indexing, Workholding, Manufacturing process, Lathe Machine

MACHINE DRAWING

Year: 2019

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE305

Topics: machine, machine parts, CAD, EDA, MDA, isometric drawing, ratchet

Polymer processing engineering technology

Year: 2020

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: PTE521

Topics: Plastics machining, machinability, polymer processing engineering technology, design, manufacturing composite, specific cutting force

POLYMER PROCESSING TECHNOLOGY 2-2013,2015,2019

Year: 2019

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: PTE401

Topics: MATLAB, mathematical modeling, extrusion, reaction, polurethane foam, adhesive, plastic, foam

Books related to Computer aided design and computer and computer aided manufacture

Computer Aided Design/Computer Aided Manufacturing

Author: Gerald Onuoha

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE505

Topics: Computer Aided Design, Computer Aided Manufacturing, computer integrated manufacturing, computer aided techniques, flexible manufacturing system, CNC programming, Lathe operation, CNC milling chamfering

Manufacturing Engineering And Technology, Seventh Edition

Author: Steven Schmid, Serope Kalpakjian

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MCE304

Topics: structure of metals, mechanical behavior of metals, manufacturing properties of metals, metal alloys, heat treatment, ferrous metals, alloy, Nonferrous metals, alloys, polymers, ceramic, glass, graphite, diamond, nano materials, composite materials, metal-casting processes, metal-casting equipment, metal casting, metal-rolling, metal-forging, metal extrusion, drawing processes, sheet-metal forming processes, powder metal, superconductors, plastics, rapid-prototyping processes, machining, cutting-tool materials, cutting fluids, machining processes, machining centers, machine-tool structures, machining economics, abrasive finishing, finishing operations, micromanufacturing, microelectronics devices, solid-welding processes, brazing, soldering, adhesive-bonding, mechanical fastening, surface technology, engineering metrology, instrumentation, quality assurance, computer-integrated manufacturing, computer-aided manufacturing

Digital Logic Circuit Analysis and Design

Author: Victor Nelson, Troy Nagle, Bill Carroll, David Irwin

School: Edo University

Department: Engineering

Course Code: EEE314

Topics: Digital Logic Circuit Analysis, Digital Logic Circuit Design, computing, digital systems, number systems, positional notation, arithmetic, binary arithmetic, octal arithmetic, hexadecimal arithmetic, base conversions, signed number representation, computer codes, numeric codes, error detection codes, correction codes, Boolean algebra, Venn diagram, Duality, switching functions, truth tables, switching circuits, electronic logic gates, combinational circuits, algebraic methods, combinational logic circuits, computer aided design, design cycle, digital circuit modelling, design synthesis, logic simulation, Karnaugh maps, Quine-McCluskey tabular minimization method, Petrick's algorithm, computer aided minimization of switching functions. Modular combinational logic, Decodes, encoders, decoder circuit structures, encoders, multiplexers, demultiplexers, data distributors, adder circuits, comparators, semi custom logic devices, logic array circuits, field-programmable logic arrays, programmable read-only memory, programmable array logic, sequential devices, sequential circuits, memory devices, latches, flip-flops, timing circuits, modular sequential logic shift registers, counters, serial adder unit, serial accumulators, parallel accumulators, multiple-sequence counters, digital fractional rate multipliers, synchronous sequential circuit models, synchronous sequential circuits, registered programmable logic device, programmable gate arrays, sequential circuit design, logic circuit testing, digital logic circuit testing, combinational logic circuit testing, sequential logic circuit testing, electronic slot machine, keyless auto entry system

Geometric and Engineering Drawing

Author: Kenneth Morling

School: Federal University, Oye-Ekiti

Department: Engineering

Course Code: MEE207

Topics: Geometric Drawing, Engineering Drawing, scales, Representative Fraction, plain scales, diagonal scales, proportional scales, triangle, quadrilateral, polygons, Isometric Projection, Conventional Isometric Projection, Isometric Drawing, tangency, Oblique Projection, loci, Trammels, Orthographic Projection, First Angle Orthographic Projection, Third Angle Orthographic Projection, prisms, pyramids, cylinders, cones, Auxiliary Elevations, Auxiliary Plans, Conic Sections, Ellipse, Parabola, Hyperbola, Fillet Curves, straight line, inclined plane, oblique plane, developments, prisms, cylinders, cones, Cycloid, trochoid, involute, Archimedean Spiral, helix, Freehand Sketching, Pictorial Sketching, Simple Cam Design, Screw Threads, Dimensioning, Conventional Representations, Framing, Title Block, Assembly Drawings

Textbook of Engineering Drawing ,2nd edition

Author: Venkata Reddy

School: University of Nigeria, Nsukka

Department: Engineering

Course Code: MEC211

Topics: Engineering Drawing, Drawing Instruments, drawing Accessories, Lettering, Dimensioning, scales, geometrical construction, Orthographic Projections, projection of solids, development of surfaces, intersection of surfaces, isometric projection, Oblique Projection, Perspective Projection, Sections of Solids, freehad sketching, Computer Aided Design and Drawing

Concrete Technology Theory and Practice, Multicolour Edition

Author: MS Shetty

School: Bayero University, Kano

Department: Engineering

Course Code: CIV5307

Topics: Concrete technology, Cements, Modern cements history, Portland cement manufacturing, Portland cement wet process manufacturing, Portland cement dry process manufacturing, Cement chemical composition, Cements hydration, Heat of hydration, Calcium silicate hydrates, Calcium hydroxide, calcium aluminate hydrates, hydrated cements structure, Water requirement for hydration, Cement types, ASTM cements classification, Ordinary Portland cement, Rapid hardened cement, Extra rapid hardening cement, Portland slag cement, Quick setting cement, super sulphated cement, low heat cement, Portland pozzolana cement, coloured cement, hydrophobic cement, masonry cement, expansive cement, Cement testing, Aggregates, aggregates testing, Aggregates form igneous rock, aggregates from sedimentary rocks, aggregates from metamorphic rock, aggregate crushing value, aggregates impact value, aggregate abrasion value, Deval attrition test, Dorry Abrasion test, Los Angeles test, modulus of elasticity, bulk density, specific gravity, Sieve analysis, Aggregates testing, Water, water qualities, Sea water for mixing concrete, Admixture, construction chemicals, Plasticizers, water reducers, Workability, Plasticizers action, Superplasticizers classification, Factors affecting workability, Superplasticizers types, Fresh concrete, Fresh concrete water content, Fresh concrete mix proportions, Aggregates sizes in fresh concrete, Aggregates shape, Surface texture, Admixture use in fresh concrete, Workability measurement, Slump test, k-slump test, aggregates grading, compacting factor test, flow test, flow table apparatus, vee bee consistometer test, setting of concrete, Manufacture of concrete process, Concrete compaction, Concrete curing, Concrete strength, Water-cement ratio, Strength gaining with age, Concrete maturity concept, Bond strength, High strength concrete, Elasticity, Creep, Shrinkage, Aggregates elastic properties, Modulus of Elasticity, Dynamic modulus of elasticity, Poison's ratio, Creep rheological representation, Creep measurement, Factors affecting creep, Aggregate influence, Mix proportion influence, Shrinkage, Plastic Shrinkage, Drying Shrinkage, Moisture movement, Autogenous Shrinkage, Carbonation shrinkage, Concrete Durability, Strength to Durability relationship, Concrete volume change, Durability definition, durability significance, Permeability, Cement paste permeability, Concrete permeability, Plastic shrinkage cracks, Settlement cracks, Thermal shrinkage, Hardened concrete testing, Concrete mix design, Special concrete, concrete methods

Machine Drawing, 3rd Edition

Author: KL Narayana, P Kannaiah, K Venkata Reddy

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE305

Topics: graphic language, principles of drawing, drawing sheet, scales, lettering, lines, sections, conventional representation, dimensioning, orthographic projection, sectional views, screwed fasteners, keys, cotters, pin joints, shaft coupling, pipe joint, pulley, riveted joints, welded joints, bearings, chains, gears, jigs, fixtures, limit, tolerances, fits, surface roughness, blue print reading, assembly drawings, part drawings, production drawing, computer aided drawing

Thinking Arabic Translation

Author: James Dickins, Sandor Hervey, Ian Higgins

School: National Open University of Nigeria

Department: Arts and Humanities

Course Code: ARA284

Topics: Arabic Translation, Arabic inter-semiotic translation, Arabic intralingual translation, interlinear translation, Arabic literal translation, Arabic free translation, communicative translation, equivalence translation loss, controlling translation loss, cultural transposition, exoticism, calque, cultural transplantation, cultural borrowing, transliterating names, compensation, denotative meaning, synonym, Hyperonymy-hyponymy, Partially overlapping translation, Connotative meaning, Attitudinal meaning, Associative meaning, Affective meaning, Allusive, reflected meaning, Alliteration, assonance, rhyme, Onomatopoeia, Translating Arabic verse, grammatical level, Grammatical arrangement, Morphological repetition, Pattern repetition, Lexical repetition, Sentence splitting, Textual restructuring, Paragraphing, Metaphor, Dead metaphors, Metaphor downtoning, tonal register, Diglossia, Translating technical texts

Engineering Drawing

Author: EPHTI

School: University of Nigeria, Nsukka

Department: Engineering

Course Code: MEC211

Topics: Engineering Drawing, Graphic Communication, Drawing Equipments, lettering, geometric construction, projection, isometric drawing, Orthographic Projection, sectioning, Dimensioning, mapping, Building Drawing

Research methodology methods and techniques, 2nd revised edition

Author: CR Kothari

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: ABE401

Topics: Research methodology, research, research methods, research process, research problem, research design, sampling design, census, sample survey, measurement, scaling techniques, scaling, scaling construction techniques, data collection, observation method, case study method, measures of central tendency, measures of dispersion, measures of asymmetry, skewness, simple regression, regression analysis, multiple correlation, regression, partial correlation, sampling, sampling distributions, central limit theorem, sampling theorem, Sandler's A-test, estimation, sample size, hypothesis, hypothesis testing, Chi-square test, Yates correction, ANOVA, analysis of variance and co-variance, ANOVA technique, analysis of Co-variance, ANOCOVA, nonparametric test, distribution free test

Advanced Engineering Mathematics ,10th Edition

Author: Erwin Kreyszig, Herbert Kreyszig, Edward

School: University of Nigeria, Nsukka

Department: Engineering

Course Code: MTH207

Topics: Ordinary Differential Equations, Separable Ordinary Differential Equations, exact Ordinary Differential Equations, linear Ordinary Differential Equations, Orthogonal Trajectories, Homogeneous Linear Ordinary Differential Equations, Differential Operators, Euler–Cauchy Equations, Higher Order Linear Ordinary Differential Equations, nonlinear Ordinary Differential Equations, Power Series, egendre’s Equation, Legendre Polynomials, Extended Power Series, Frobenius Method, Bessel’s Equation, Bessel Functions, Laplace Transforms, First Shifting Theorem, Linear Algebra, Vector Calculus, Matrices, Vectors, Determinants, Linear Systems, Determinants, Cramer’s Rule, Gauss–Jordan Elimination, linear transformation, Matrix Eigenvalue Problems, Eigenvalues, Eigenvectors, Eigenbase, Vector Differential Calculus, vector product, Vector Integral Calculus, Integral Theorems, line integrals, Surface Integrals, Stokes’s Theorem, Fourier Analysis, Partial Differential Equations, Fourier series, Sturm–Liouville Problems, Forced Oscillations, Fourier Integral, Fourier Cosine, Sine Transforms, Fourier Transform, Fast Fourier Transforms, Rectangular Membrane, Double Fourier Series, heat equation, Complex Numbers, Complex Differentiation, Cauchy–Riemann Equations, Exponential Function, Complex Integration, Cauchy’s Integral Formula, Cauchy’s Integral Theorem, Taylor series, Laurent Series, Residue Integration, Conformal Mapping, Complex Analysis, Potential Theory, Numeric Analysis, Numeric Linear Algebra, Unconstrained Optimization, Linear Programming, Combinatorial Optimization, Probability, Statistics, Data Analysis, Probability Theory, Mathematical Statistics

Advanced Engineering Mathematics Student Solutions Manual and Study Guide,10th edition Volume 1&2

Author: Herbert Kreyszig, Erwin Kreyszig

School: University of Nigeria, Nsukka

Department: Engineering

Course Code: MTH207

Topics: Ordinary Differential Equations, Separable Ordinary Differential Equations, exact Ordinary Differential Equations, linear Ordinary Differential Equations, Orthogonal Trajectories, Homogeneous Linear Ordinary Differential Equations, Differential Operators, Euler–Cauchy Equations, Higher Order Linear Ordinary Differential Equations, nonlinear Ordinary Differential Equations, Power Series, egendre’s Equation, Legendre Polynomials, Extended Power Series, Frobenius Method, Bessel’s Equation, Bessel Functions, Laplace Transforms, First Shifting Theorem, Linear Algebra, Vector Calculus, Matrices, Vectors, Determinants, Linear Systems, Determinants, Cramer’s Rule, Gauss–Jordan Elimination, linear transformation, Matrix Eigenvalue Problems, Eigenvalues, Eigenvectors, Eigenbase, Vector Differential Calculus, vector product, Vector Integral Calculus, Integral Theorems, line integrals, Surface Integrals, Stokes’s Theorem, Fourier Analysis, Partial Differential Equations, Fourier series, Sturm–Liouville Problems, Forced Oscillations, Fourier Integral, Fourier Cosine, Sine Transforms, Fourier Transform, Fast Fourier Transforms, Rectangular Membrane, Double Fourier Series, heat equation, Complex Numbers, Complex Differentiation, Cauchy–Riemann Equations, Exponential Function, Complex Integration, Cauchy’s Integral Formula, Cauchy’s Integral Theorem, Taylor series, Laurent Series, Residue Integration, Conformal Mapping, Complex Analysis, Potential Theory, Numeric Analysis, Numeric Linear Algebra, Unconstrained Optimization, Linear Programming, Combinatorial Optimization, Probability, Statistics, Data Analysis, Probability Theory, Mathematical Statistics

Manual of Engineering Drawing ,4th edition

Author: Colin Simmons, Dennis Maguire, Neil Phelps

School: University of Nigeria, Nsukka

Department: Engineering

Course Code: MEC211

Topics: Drawing Office Management, Product Development, Computer Aided Design, Intellectual Property, Engineering Design, CAD Organization, CAD Applications, First Angle Orthographic Projection, Third Angle Orthographic Projection, Engineering Drawing, linework, lettering, Three-dimensional Illustrations, Sections, Sectional Views, Geometrical Constructions, Tangency, Loci Applications, Conic Sections, Interpenetration of Solids, Dimensioning Principles, Screw Threads, Conventional Representations, Nuts, Bolts, Screws, Washers, limits, fits, Geometrical Tolerancing, Datums, Maximum Material Principle, Least Material Principle, Positional Tolerancing, surface texture, surface finish, corrosion, 3D annnotation, duality principle, cams, gears, spring, welding, welding symbols, engineering diagrams, bearing, Engineering Adhesives, production drawings

Design of structural elements, 3rd Edition

Author: Chanakya Arya

School: Bayero University, Kano

Department: Engineering

Course Code: CIV3307, CIV4204, CIV5405

Topics: Structural Design, Design Philosophy, Design Basics, Basic structural concepts, materials properties, Design loads acting on structures, Design loads acting on elements, Structural analysis, Beam design, Column design, British Standard Structural design, Beams, Slabs, Foundations, Retaining walls, Design in structural steelwork to BS5950, Iron, Steel, Design Strength, Connections Design, Design in unreinforced masonry, Design in timber to BS5268, Structural design to Eurocodes

Teaching and Researching Translation, 2nd edition

Author: Basil Hatim

School: National Open University of Nigeria

Department: Arts and Humanities

Course Code: ARA383

Topics: Teaching Translation, Researching Translation, translation studies, applied linguistics, translation analyst, reflective practice, Bridging cultural and linguistic differences, pragmatics, translator invisibility, gendered translation, metatext, literary, Polysystem theory, Manipulationists, translation purpose, Translation strategy dichotomies assessed, Translation strategy, relevance theory, text procesning, genre, genre norms, discourse practices, literal translation

Interpreting Engineering Drawings

Author: Theodore Branof

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: MEE305

Topics: line types, sketching, lettering, title blocks, circle, arcs, working drawings, projection theory, dimensioning, normal surface, inclined surface, oblique surface, pictorial sketching, machining symbols, revision blocks, chamfers, undercuts, tapers, knurls, sectional views, surface texture, conventional tolerancing, inch fits, metric fits, threads, auxiliary views, development drawings, piping drawings, bearings, manufacturing materials, casting processes, violating true projections, pin fasteners, numerical control, assembly drawings, structural steel, welding drawings, groove welds, spur gears, bevel gears, gear trains, cams, bearings, clutches, ratchet wheels, geometric dimensioning, form tolerances, datum reference frame, orientation tolerances, datum targets, position tolerance, profile tolerance, runout tolerance

Logic circuit

Author: DK Kaushik

School: Federal University of Technology, Minna

Department: Engineering

Course Code: EEE211

Topics: number system, binary number system, octal number system, hexadecimal number system, binary addition, binary subtraction, signed numbers, complement representation, binary multiplication, floating point representation, binary codes, binary coded decimal numbers, weighted codes, self implementing codes, cyclic codes, gray code, error detecting codes, error correcting code, Hamming code, BCD addition, alphanumeric codes, Boolean algebra, logic gates, duality principle, Venn diagram, truth table, Karnaugh map, Quine – McCluskey Method, combinational switching circuits, combinational circuits, half adder, full adder, parallel binary adder, 8421 adder, BCD adder, subtractor, multiplexers, demultiplexers, code converter, encoders, priority encoder, magnitude comparator, parity generator, parity checker, programmable logic devices, Field Programmable Logic Array, Programmable Array Logic, Programmable Read Only Memory, Direct Coupled Transistor Logic, Integrated Injection Logic, transistor transistor logic, CMOS Logic, Flip flop, shift registers, counter, Asynchronous Counters, counter ICs, Digital to Analog Converter, Analog to Digital Converter, digital memory, semiconductor memory, read only memory, random access memory, magnetic memory, magnetic bubble memories, charged coupled devices, compact disk read only memory

Engineering Drawing I

Author: Chibeoso Wodi

School: University of Nigeria, Nsukka

Department: Engineering

Course Code: MEC211

Topics: Engineering Drawing, Engineering Drawing Instruments, Lettering, Descriptive Geometry, Geometric Constructions, tangency, Dimensioning, Conventions, Orthographic Projections, Isometric Projections, sectioning, loci, development, freehand sketching, machine drawing

Fundamentals of Vehicle Dynamic

Author: Thomas Gillespie

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: ATE503

Topics: Vehicle Dynamic, Dynamic Axle Loads, acceleration performance, power-limited acceleration, power train, automatic transmissions, braking forces, brakes, tire-road factor, Brake Proportioning, Anti-Lock Brake Systems, braking efficiency, rear wheel lockup, pedal force gain, road loads, aerodynamics, aerodynamic forces, Aerodynamics Aids, Rolling Resistance, Vehicle Response Properties, Low-Speed Turning, steady-state cornering, suspension, Anti-Pitch Suspension Geometry, MacPherson Strut, Roll Center Analysis, Solid Axle Roll Centers, Independent Suspension Roll Centers, active suspensions, steering system, Steering Geometry Error, Steering System Forces, Steering System Models, Four-Wheel Steer, rollover, tires, Tire Construction, Camber Thrust, Combined Braking, Cornering, Durability Forces

Advanced engineering mathematics

Author: Ken Stroud, Dexter Booth

School: Federal University of Technology, Owerri

Department: Engineering

Course Code: ENG307, ENG308

Topics: Advanced engineering mathematics, numerical solution, Newton-Raphson iterative method, numerical methods, linear interpolation, graphical interpolation, Lagrange interpolation, Laplace transform, convolution theorem, periodic functions, Z transform, difference equations, Invariant linear systems, Differential equations, Fourier series, harmonics, Dirichlet conditions, Gibbs’ phenomenon, Complex Fourier series, complex spectra, Fourier’s integral theorem, Leibnitz-Maclaurin method, power series, Cauchy-Euler equi-dimensional equations, Leibnitz theorem, Bessel’s equation, Gamma functions, Bessel functions, Legendre’s equation, Legendre polynomials, Rodrigue’s formula, Sturm-Liouville systems, Orthogonality, Taylor’s series, First-order differential equations, Euler's method, Runge-Kutta method, Matrix algebra, Matrix transformation, Eigenvalues, direction fields, phase plane analysis, nonlinear systems, dynamical systems, Bifurcation, partial differentiation, Elliptic equations, Hyperbolic equations, Parabolic equations, multiple integration, Green’s theorem, integral functions, error function, elliptic functions, vector analysis, Curvilinear coordinates, complex analysis, complex mapping, Maclaurin series, optimization, linear programming, Linear inequalities