|Field of Study||Mathematics|
|Delivery Method||Offline (100% offline course):|
Calculus is essential for natural science and engineering. This course presents parts of calculus, differentiation and integration of several functions including polar curves.
We will calculate various quantities, such as arc lengths and areas of the surface of revolution. In addition, we will learn how to determine the convergence of various series and how we can expand functions using power series.
Basic knowledge for algebra.
Materials: Calculus 8E (Metric version, Early transcendentals) by James Stewart.
Class 1: Introduction and basics
Class 2: 1.5 Inverse functions 2.4 The precise definition of a limit (shortly)
Class 3: 3.5 Implicit differentiation 3.10 Linear approximation and Differentials
Class 4: 3.11 Hyperbolic functions 4.1 Maximum and minimum values 4.2 Mean value theorem
Class 5: 4.4 Indeterminate form and l’Hospital’s rule 4.7 Optimization problems 4.8 Newton’s theorem
Class 6: 5.2 Definite integral 5.3 Fundamental theorem of calculus 5.5 Substitution rule
Class 7: 6.2 Volumes 6.3 Volumes by cylindrical shells 6.5 Average value of a function
Class 8: Midterm Exam
Class 9: 7.1 Integration by parts 7.2 Trigonometric integrals 7.3 Trigonometric substitution 7.4 Integration of rational functions by partial fractions
Class 10: 7.8 Improper integrals 8.1 Arc length 8.2 Area of a surface of revolution
Class 11: 10.2 Calculus with parametric curves 10.3 Polar coordinates 10.4 Calculus in polar coordinates
Class 12: 11.1 Sequences 11.2 Series 11.3 Integral test 11.4 Comparison test
Class 13: 11.5 Alternating series and absolute convergence 11.6 Ratio and root tests 11.8 Power series
Class 14: 11.9 Representation of functions as power series 11.10 Taylor and Maclaurin series 11.11 Applications of Taylor polynomials
Class 15: Final exam
|Last Updated||November 1, 2021|