Mathematics I

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