UNIVERSITY OF BRITISH COLUMBIA
MATH 105-SECTION 205
SPRING 2015
Integral Calculus with Applications to Commerce and Social Sciences
Textbook: Calculus: Early Transcendentals, Volume 2. Fourth custom edition for UBC, by Briggs and
Cochran. The textbook is available at the UBC Bookstore. ISBN 10 digit: 1269921924. ISBN 13 digit:
9781269921923. This book is available at the UBC Bookstore.
Grading Scheme:
• Final Exam 50%
• Two One-Hour Midterms 17% + 17% = 34%
– Midterm exam 1 will be held on January 29, 2014 (Thursday). The time is from 6:30pm
to 7:30pm
– Midterm exam 2 will be held on March 18, 2014 (Wednesday). The time is from 6:30pm
to 7:30pm
• Course-common WebWorks assignments 10%
• Quizzes 6% : There will be 10-15minutes quizzes in class weekly(8 quizzes totally) on each Wednesday. First quiz will be on January 14, 2015. Each quiz has 10 points, in the end your quiz part
grade will be equal to min(the sum of 8 quizzes/10, 6).
Section 205 Instructor: Dr. Mingfeng Zhao, ESB 4122, phone 604-822-2159, mingfeng@math.ubc.ca.
Office Hours Location: Leonard S. Klinck Building 300C
Office Hours: Monday & Tuesday & Wednesday 01:30PM–02:30PM or By Appointment
Section 205 homepage: http://www.math.ubc.ca/~mingfeng/integralspring2015.html
Piazza Signup Link: http://piazza.com/ubc.ca/winterterm22014/math105section205
Weekly Topics:
Roughly speaking, we will cover multivariable calculus (Chapter 12) and start on integration (Chapter 5)
before the first midterm. We will complete the theory of integration (Chapter 5) and integration techniques
(Chapter 7), followed by a week’s worth of probability before the second midterm. The rest of the time
will be devoted to discussing sequences and series (Chapters 8 and 9).
1. Dot products(Chapter 11) and Functions of several variables (Chapter 12)
• Dot products (11.3)
• Planes and surfaces (12.1)
• Graphs and level curves (12.2)
2. Functions of several variables (Chapter 12)
• Partial derivatives (12.4)
• Maximum/minimum problems (12.8)
3. Functions of several variables (Chapter 12)
• Maximum/minimum problems (12.8)
• Lagrange multipliers (12.9)
4. Integration (Chapter 5)
• Approximating areas under curves (5.1)
• Definite integrals (5.2)
5. Integration (Chapter 5)
• Fundamental theorem of calculus (5.3)
• Substitution rule (5.5)
• Integration by parts (7.2)
6. Integration techniques (Chapter 7)
• Trigonometric Integrals (7.3)
• Trigonometric substitutions (7.4)
• Partial fractions (7.5)
7. Integration techniques (Chapter 7)
• Numerical integration (7.7)
• Improper integrals (7.8)
• Introduction to differential equations (7.9)
8. Probability ( Probability Appendix)
• Random Variables and Probability Basics ( 1.1, 1.2 and 1.4 in Probability Appendix)
• Continuous random variable ( 2.1 and 2.2 in Probability Appendix)
• Expected Value, Variance, and Standard Derivation (2.5 and 2.6 in Probability Appendix)
9. Sequences and infinite series (Chapter 8)
• Sequences (8.1-8.2)
• Infinite series (8.3)
• The divergence and integral tests (8.4)
10. Series (Chapter 8) and Power series (Chapter 9)
• The ratio, root and comparison tests (8.5)
• Approximating functions with polynomials (9.1)
• Properties of power series (9.2)
11. Power series (Chapter 9) and review
• Taylor series (9.3)
• Working with Taylor series (9.4)
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