# Calculus IB (Math 1013)

### Meeting Time and Venue:

Tuesday & Thursday, 10:30AM-11:50AM   (please find the zoom meeting in CANVAS-HKUST)

### Course Description:

This is an introductory course in one-variable calculus. Topics include functions and graphs, limits of functions and continuity, derivatives and their applications, basic indefinite and definite integrals. Upon successful completion of this course, students should be able to: 1. develop basic computational skills in calculus; 2. express quantitative relationships using the language of functions; 3. apply the concepts and methods of calculus in modeling and problem solving.

• Jishan Hu, Weiping Li and Yueping Wu. "Calculus for scientists and engineers with MATLAB". [Classviva]
• James Stewart. "Single variable calculus: Early transcendentals". Cengage Learning, 2015. [Amazon]

### Courseware (subject to changes):

• All lecture slides with single file: [pdf].
• The tutorial notes provided by TA Yulin Hu [pdf] and TA Phyllis, Shi-Xin Liang [link].
• Sep 08: Sets, Intervals, Inequalities, Absolutes, Functions. [pdf]
• Sep 10: Basic of Functions, Graphs, Composite Functions. [pdf]
• Sep 15: Inverse Functions, Exp/Log Functions, Trigonometric Functions. [pdf]
• Sep 17: Trigonometric/Inverse Trigonometric Functions, Slope of Tangent Line, Limit and Natural Exp/Log Functions. [pdf]
• Sep 22: Slope and Derivative, Precise Definition of Limit. [pdf]
• Sep 24: Limits of Function Values, Asymptotes and Limits at Infinity, Limit Laws. [pdf]
• Sep 29: Limit Laws, Extended Real Number System, Squeeze Theorem. [pdf]
• Oct 01: National Day (No Classes)
• Oct 06: Continuity of Functions, Intermediate Value Theorem, Basics of Derivatives. [pdf]
• Oct 08: Basic Formulas of Derivatives, Rules of Differentiation, Chain Rule. [pdf]
• Oct 13: Typhoon Signal No. 8 (No Classes)
• Oct 15: Derivatives of Trigonometric Functions, Derivatives of Inverse Functions, Implicit Differentiation. [pdf]
• Oct 20: Rates of Change, Higher-Order Derivatives. [pdf]
• Oct 22: Extreme Values of Functions, Mean Value Theorem, Derivatives and Graphs. [pdf]
• Oct 27: Convexity/Concavity and 2nd Derivatives, Graph Sketching. [pdf] [Code 1] [Code 2]
• Oct 29: Optimization Problems, Characterization of Convexity/Concavity, Properties of Convex Functions. [pdf]
• Nov 03: Geometric View and Global Minimum of Convex Functions, Linear Approximation. [pdf]
• Nov 05: L'Hôpital's Rule, Convex Optimization. [pdf]
• Nov 10: Newton's Method: Algorithm, Convergence Analysis and Application in Convex Optimization. [pdf] [Code]
• Nov 12: Antiderivatives/Indefinite Integral, The Substitution Rule, Integration by Parts. [pdf]
• Nov 17: Initial Value Problems, Area under Curve, Riemann Sums and Definite Integrals. [pdf]
• Nov 19: More Examples of Definite Integrals, Fundamental Theorem of Calculus. [pdf]
• Nov 24: The Proof of Fundamental Theorem of Calculus, Integrability, Taylor Series. [pdf]
• Nov 26: Fundamental Theorem of Calculus (v2), Net Change, Substitution Rule and Symmetry in Definite Integrals. [pdf]
• Dec 01: Course Review. [pdf]
• Dec 03: Problems in Past Sample Papers. [Past Midterm Exam, Solution, Details of MC] [Past Final Exam, Solution]
• Dec 09: Trail Exam. [Solutions]

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