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Calculus & Analytic Geometry

• Basic Concepts: Real Numbers and Real Lines
• Polar Coordinates
• Parametric Equations
• Functions, Algebra of Functions
• Inverse Functions, Quadratic Functions
• Shifting Graphs, Trigonometric Functions
• Complex Numbers, Inequalities
• Infinite Series and Sequences
• Taylor Series, Rate of Change and Limit
• Rules of Finding Limits
• Formal Definition of Limit
• Extension of the Limit Concepts
• L’Hospitals Rule
• Continuity, Tangent Lines
• Differential Calculus
• The Derivatives of a Function
• Differentiation Rules
• Rates of Change
• Derivatives of Trigonometric Functions
• Chain Rule Differentiation
• Implicit Differentiation and Rational
• Exponents, Related Rates of Change
• Extreme Values of Functions
• 1st and 2nd Derivative Tests for Extreme Values
• Optimization and Linearization
• Differentials and Newton’s Method
• Integral Calculus
• Indefinite Integrals, Integration by Substitution
• Riemann Sums, Definite Integral
• Fundamental Theorem of Calculus
• Mean Value Theorem
• Substitution in Definite Integrals
• Areas between Curves
• Finding Volumes by Slicing
• Volumes of Solids of Revolution
• Cylindrical Shells, Lengths of Plane Curves
• Areas of Surfaces of Revolution
• Moments and Center of Mass
• Fluid Pressures and Forces
• Integration by Parts
• Improper Integrals
• Multiple Integrals and Line Integrals
• Linear Algebra and Vector Calculus
• Matrices, Operation on Matrices
• Inverse of a Matrix
• Rank of Matrix
• Determinant Vectors
• Solutions of System of Linear Equations
• Eigen value Problems