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York University
AS/SC/AK/MATH 1310 3.00MW (Winter 2008)
Integral Calculus with Applications
Tentative Schedule
Week 1
- Jan 4: Review of Sections 3.2-3.4 - Riemann sums and the fundamental theorem of calculus
Week 2
- Jan 7: Section 3.5 - indefinite integrals
- Jan 9: Sections 3.5 and 3.6 - algebraic manipulations and substitution
- Jan 11: Section 3.6 - trig substitutions
Week 3
Jan 17 is the last date to enroll without permission of the instructor.
MathLab starts operation as of Jan 14.
- Jan 14: Section 3.7 - volumes
- Jan 16: Section 3.8 - volumes of revolution
- Tutorial: Quiz 1 on 3.5 and 3.6 (not including trig substitutions)
- Jan 18: Section 3.8 - numerical methods
Week 4
Jan 25 is the last date to enroll even with permission of the instructor.
- Jan 21: Section 3.9 - physics applications
- Jan 23: Section 4.2 - review of exponentials and logarithms
- Tutorial: Quiz 2 on 3.7 (not including shells)
- Jan 25: Sections 4.2 and 4.3 - exponentials and logs
Week 5
- Jan 28: Sections 4.3 and 4.4 - logs, integration by parts formula
- Jan 30: Section 4.4 - integration by parts examples
- Tutorial: Review session for midterm
- Feb 1: 4.5 - more trig substitutions
Week 6
- Feb 4: 4.6, 4.7 - reverse trig substitutions, rational functions
- Feb 6: 4.7 - rational functions
- Feb 8: 4.7, 4.9 - rational functions, improper integrals
Week 7
Reading week - no classes.
Week 8
- Feb 18: Holiday - no classes.
- Feb 20: 4.9 - improper integrals
- Tutorial: Quiz 3, on 4.4 (integration by parts)
- Feb 22: 4.9 - improper integrals
Week 9
- Feb 25: 4.11 - Differential equations
- Feb 27: 4.11, 5.2 - Differential equations, sequences
- Tutorial: Quiz 4, on 4.7 (integration of rational functions)
- Feb 29: 5.2, 5.3 - sequences, limits
Week 10
Mar 7 is the last day to drop the course.
- Mar 3: 5.4 - infinite numerical series (We'll return to the power series material from this section later in the course): convergence, divergence, geometric series
- Mar 5: 5.4 - telescoping series, nth term test, series of positive terms
- Tutorial: Review session for midterm
- Mar 7: 5.4, 5.9 - comparison test, absolute and conditional convergence
Week 11
- Mar 10: 5.9 - integral test
- Mar 12: 5.9, 5.7 - limit comparison test, ratio test
- Mar 14: 5.9 - alternating series test
Week 12
- Mar 17: 5.4, 5.5 - simple power series, Taylor series
- Mar 19: 5.5 - Taylor polynomials (with error estimates)
- Tutorial: Quiz 5 - numerical series (5.4, 5.9)
- Mar 21: Holiday - no classes
Week 13
- Mar 24: 5.5 - Applications of Taylor's theorem
- Mar 26: 5.5 - Taylor series, binomial series
- Tutorial: Quiz 6: Taylor polynomials (5.5)
- Mar 28: 5.6 - General Taylor theorem and applications
Week 14
- Mar 31: 5.7 - Power series
- Apr 2: 5.7 - Power series
- Tutorial: Review/problem session (given by Salisbury)
- Apr 3: Makeup class - course review
- Apr 4: Problem session (given by Ma Jianfu (TA))
Week 15
Exams begin