Mathematics Topic-wise Tests & Solved Examples for IIT JAM MathematicsMathematics Vector Calculus- Introduction to vectors
- Vector operations: addition, subtraction, scalar multiplication
- Dot product and cross product
- Vector functions and their derivatives
- Line integrals and surface integrals
- Green's theorem, Gauss's theorem, and Stokes' theorem
Mathematics Sequences and Series of Real Numbers- Arithmetic sequences and series
- Geometric sequences and series
- Convergence and divergence of sequences
- Convergence and divergence of series
- Tests for convergence: comparison test, ratio test, root test
- Power series and Taylor series
Mathematics Matrix- Introduction to matrices
- Matrix operations: addition, subtraction, scalar multiplication, matrix multiplication
- Determinants and their properties
- Inverse of a matrix
- Systems of linear equations and matrix equations
- Eigenvalues and eigenvectors
Mathematics Linear Transform- Definition and properties of linear transformations
- Matrix representation of linear transformations
- Kernel and image of a linear transformation
- Change of basis and similarity transformations
- Diagonalization and Jordan form
Mathematics Group Theory- Definition and properties of groups
- Subgroups, cosets, and quotient groups
- Group homomorphisms and isomorphisms
- Cayley's theorem and permutation groups
- Group actions and orbit-stabilizer theorem
- Solvable and simple groups
Mathematics Differential Equation- First-order ordinary differential equations
- Second-order ordinary differential equations
- Higher-order ordinary differential equations
- Systems of ordinary differential equations
- Laplace transforms and their applications
- Partial differential equations
Mathematics Integrals- Definite integrals and their properties
- Indefinite integrals and antiderivatives
- Techniques of integration: substitution, integration by parts, partial fractions
- Improper integrals
- Applications of integration: area, volume, work, arc length
Mathematics Real Analysis- Real numbers and their properties
- Sequences and limits of real numbers
- Continuity and differentiability of real functions
- Mean value theorem and intermediate value theorem
- Riemann integration and fundamental theorem of calculus
- Metric spaces and compactness
Mathematics Indeterminate Form- Evaluation of limits involving indeterminate forms
- L'Hospital's rule and its applications
- Infinite series and their convergence
- Power series and their convergence
- Taylor and Maclaurin series
Mathematics Linear Algebra- Vector spaces and subspaces
- Basis and dimension of a vector space
- Linear independence and span
- Linear transformations and their matrix representations
- Eigenvalues and eigenvectors
- Inner product spaces and orthogonal projections
Mathematics Permutations and Combinations- Permutations and combinations: counting principles
- Binomial coefficients and Pascal's triangle
- Multinomial coefficients
- Permutations with restrictions
- Combinations with repetitions
- Generating functions
Mathematics Trigonometric Functions and Identities- Trigonometric functions: sine, cosine, tangent, etc.
- Trigonometric identities: Pythagorean identities, sum and difference identities, double angle identities
- Inverse trigonometric functions
- Trigonometric equations and their solutions
- Trigonometric substitutions in integrals
Mathematics Probability and Statistics- Probability: basic concepts, sample space, events
- Conditional probability and independence
- Random variables and probability distributions
- Discrete and continuous probability distributions
- Expected value and variance
- Statistical inference: estimation and hypothesis testing
Mathematics Binomial Theorem- Binomial coefficients and Pascal's triangle
- Expansion of binomial expressions
- Applications of binomial theorem
- Binomial probability distributions
- Binomial series and its convergence
Mathematics Dimensional Geometry- Coordinate systems in two and three dimensions
- Equations of lines and planes
- Distance and midpoint formulas
- Intersection of lines and planes
- Vectors in three-dimensional space
- Dot product and cross product in three-dimensional space
Mathematics Integral Calculus- Definite integrals and their properties
- Indefinite integrals and antiderivatives
- Techniques of integration: substitution, integration by parts, partial fractions
- Improper integrals
- Applications of integration: area, volume, work, arc length
Mathematics Functions of One, Two or Three Real Variables- Limits and continuity of functions
- Differentiation of functions
- Applications of derivatives: optimization, curve sketching
- Integration of functions
- Multiple integrals and their applications
- Partial derivatives and their applications
This course is helpful for the following exams: IIT JAM, Mathematics