Topics: fundamental quantities, derived quantities, dimension, scalars, vectors, vector representation, unit vectors, vector multiplication, kinematics, displacement, speed, velocity, acceleration, freely falling bodies, projectile motion, horizontal projectile motion, Newton's laws of motion, elastic collision, inelastic collision, friction, circular motion, gravitation, angular speed, angular acceleration, conical pendulum, Banking, free-fall acceleration, gravitational potential energy, satellite motion, velocity escape, Kepler's law, work, energy, power, energy conversion, Kinetic energy, conservative forces, vector moment, mechanical equilibrium, rigid bodies rotation, moment of Inertia, Parallel Axis theorem, Hooke's law, stress, strain, density, fluid mechanics, fluid pressure, Pascal's Principle, Buoyancy principle, Archimedes Principle. fluid dynamics, Bernoulli principle, surface tension, Poiseuille's law, capillarity, Stoke's law, thermal physics, temperature scales, thermometers, Zeroth law of thermodynamics, thermal expansion, thermal stress, heat quantity, Latent heat, heat transfer, conduction, convection, radiation, Gas laws, Kinetic theory of gases, Thermodynamic processes, Adiabatic processes, Isobaric processes, Isochoric processes, Thermal efficiency, Carnot cycle, Refrigerator, Entropy

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

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

Topics: Chemistry Calculations, Masses and Formulae, Relative Atomic and Molecular Masses, Mass Percentage Composition, Valency, Chemical Formula, Empirical and Molecular Formulae, Reduced Mass, Chemical Reaction, Stoichiometry, Mole, Chemical Equations, Reaction Stoichiometry, Chemical Laws, Redox Reactions, IUPAC Nomenclature, Oxidation Number, Redox Equations, IUPAC Nomenclature of Inorganic Substances, Atomic Structure, Chemical Bonding, Dalton’s Atomic Theory, Wave-Particle Duality of Matter, Uncertainty Principle, Ionization Energy, Ionic Bond, Lattice Energy, Covalent Bond, Heat of Reaction, Dipole Moment, Formal Charge, The Gaseous State, Gas Pressure, Gas Laws, Critical Constants of Gases and Equations of State for Real Gases, Reduced State Properties, Gas Density, Gas Stoichiometry, Molar Volume of Gases, Relative Vapour Density, Gas diffusion, Mole Fraction, Kinetic Theory of Gases, The Solid and Liquid States, Vapour Pressure, Change of State, Density of Solids, X-Ray Crystallography, Determination of Viscosity of Liquids from Stokes’ Law, Surface Tension, Properties of Solutions, Concentration, Molality, Solubility, Solubility Product, Colligative Properties of Solutions, Conductance of Solutions, Quantitative Analysis, Volumetric Analysis, Gravimetric Analysis, Thermodynamics, Calorimetry, Heat (Enthalpy Change) of Physical Change, Heat (Enthalpy Change) of Reaction, Heat Capacities of Gases, Thermodynamics of Solutions, The First Law of Thermodynamics, The Second Law of Thermodynamics, Efficiency, Electrochemistry, Electrochemical Cells, Electrolysis, Chemical Equilibria, Le Chatelier’s Principle, Position of Equilibrium, Equilibrium Constant, Reaction Quotient, Acid-Base Equilibria, Acid Ionization Constants, Base Ionization Constants, Water Autoionization Constant, Hydrogen Ion Concentration, Buffer Solutions, Salts, Chemical Kinetics, Rates of Reactions, Rate Law, Nuclear Chemistry, Radioactivity, Nuclear Reactions