Graphs: Functions and their Graphs. Shifting and Scaling of Graphs.
Limit and Continuity: Limit (One-Sided and Two-Sided) of Functions. Continuous Functions, Discontinuities, Monotonic Functions, Infinite Limits and Limit at Infinity.
Differentiation and its Applications: Derivative of a function, non differentiability, Intermediate Value Property, Mean Value Theorem, Extreme Values of Functions, Monotonic Functions, Concavity and Curve Sketching, Integration: Definite Integrals, The Mean Value Theorem for definite integrals, Fundamental Theorem of Calculus, Integration Techniques.
Review: System of linear Equations, linear independence
Eigen values and Eigen vectors: Definitions and Properties, Positive definite, Negative Definite and Indef inite Matrices, Diagonalization and Orthogonal Diagonalization, Quadratic form, Transformation of Quadratic Form to Principal axes, Symmetric and Skew Symmetric Matrices, Hermitian and Skew Hermitian Matrices and Orthogonal MatricesIterative Methods for the Solution of Linear Systems, Power Method for Eigen Values and Eigen Vectors.