### Course Details

 Title Calculus 1 Field of Study Mathematics Professor hanyang (summerschool@hanyang.ac.kr) Type Academic course Delivery Method Offline (100% offline course): Credits 3 Contact hours 45 Schedule Course code GEN2052 Course number Description Calculus is essential for natural science and engineering. This course presents parts of calculus, differentiation and integration of several functions including polar curves. Objective 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. Preparations Basic knowledge for algebra. Materials: Calculus 8E (Metric version, Early transcendentals) by James Stewart. Materials Evaluation Assignment 10% Attendance 10% Final 40% Midterm 40% Lesson Plan 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 Print