Mathematics I

##### Course List
 Week Topic File 1 Numbers, Cartesian coordinate system, lines, circles, parabolas, ellipses and hyperbolas 1 Functions 2 Trigonometric functions, inverse functions, exponential and logarithmic functions 2 Inverse trigonometric functions and hyperbolic functions 3 The concept of limit 3 Limits involving infinity, Continuity, The Max-Min Theorem, The Intermediate Value Theorem 4 Formal definition of limit, derivatives 4 Derivative as a function, one-sided derivatives, Differentiation rules, The chain rule 5 Derivatives of trigonometric functions, using differentials 5 The Mean Value Theorem, Rolle's Theorem, Implicit Differentiation 6 Derivatives of inverse functions, Logarithmic Differentiation, Related Rates Problems 6 Finding Roots of Equations: Newton's Method, Indeterminate Forms in Limits - l'Hospital's Rule 6 Critical points, Finding absolute extreme values, Concavity 7 Sketching the graph of a function, extreme value problems 7 The area problem 8 Definite integral 8 The Fundamental Theorem of Calculus, The substitution method, trigonometric integrals 9 Areas of plane regions, integration by parts 10 Integrals of rational functions, Inverse substitution method 10 Improper Integrals, volumes 11 Arc length, surface area, infinite sequences 11 Sequences, Infinite series 12 Convergence tests 12 Power series 13 Taylor and Maclaurin series