Instructor: Shingyu Leung
Email: masyleung @ ust.hk
Office: 3491
Office hours: Wednesday 1500-1700
Class webpage: http://www.math.ust.hk/~masyleung/021.10f.html
Class blog: http://math021-2010f.blogspot.com/
TA: YU, Pubing (T3a Thur 1400-1450 2405, T3b Mon 1530-1620 LTG), LI, Wenbin (T4a Thur 1830-1920 2302, T4b Mon 1800-1850 2302)
Lectures: L3 Wednesday and Friday 1330-1450, Room LTF
Lectures: L4 Tuesday and Thursday 1500-1620, Room 4621
Textbook: Univeristy Calculus - Hass, Weir, Thomas, First edition. Chapters 1-5,7-9
Midterm: OCT 12 (Tuesday) 730pm-830pm
Final: TBA
Announcement
[Click Here]
Grading Scheme
35% Midterm
65% Final: Comprehensive, i.e. all materials taught in the whole semester will be tested,
including those already tested in the miderm exam. But focus will be on those topics not covered
in the midterm.
Exams are closed books and notes, no calculator and no formula sheets are provided.
More information will be given in the lecture prior to the exams.
Past Papers
2008 Fall Midterm Exam 2008 Fall Final Exam 2009 Fall Midterm Exam 2009 Fall Final Exam
Homework
Homework will be assigned more or less weekly. You don't have to but ARE HIGHLY ENCOURAGED
to finish it.
[Click Here]
Homework Solution
[Click Here]
Actual Schedule of Lectures
[Click Here]
Schedule of Lectures (Tentative)
Functions (Sections 1.1-1.5): 3 lectures
Functions and their graphs
Combining functions; shifting and scaling graphs
Trigonometric functions
Exponential functions
Inverse functions and logarithms
Limits and Continuity (Sections 2.1-2,4-7): 4 lectures
Rates of change and tangents to curves
Limit of a function and limit laws
One-Sided limits and limits at infinity
Infinite limits and vertical asymptotes
Continuity
Tangents and Derivatives at a point
Differentiation (Sections 3.1-10): 6 lectures
The derivative as a function
Differentiation rules for polynomials, exponentials, products, and quotients
The Derivative as a rate of change
Derivatives of trigonometric functions
The chain rule and parametrix equations
Implicit differentiation
Derivatives of inverse functions and logarithms
Inverse trigonometric functions
Related rates
Linearization and differentials
Applications of Derivatives (Section 4.1-6): 3 lectures
Extreme values of functions
The mean value theorem
Monotonic functions and the first derivative test
Concavity and curve sketching
Applied optimization
Indeterminate forms and l'hopital's rule
Integration (Section 5.1-6): 3 lectures
Estimating with finite sums
Sigma notation and limits of finite sums
The definite integral
The fundamental theorem of calculus
Indefinite Integrals and the substitution rule
Substitution and area between curves
Techniques of integration (Section 7.1-4,7): 3 lectures
Integration by parts
Trigonometric integrals
Trigonometric substitutions
Integration of rational functions by partial fractions
Improper integrals
Infinite sequences and series (Section 8.1-2,7-8): 3 lectures
Sequences
Infinite series
Power series
Taylor and Maclaurin series
Polar coordinates and conics (Section 9.1-2): 1 lectures
Polar coordinates
Graphing in polar coordinates
MATH021 Concise Calculus