MATH 101
Integral Calculus with Applications to Physical
Sciences and Engineering
Jan. 2015
Instructor: Dragos Ghioca, Math Annex 1223, dghioca@math.ubc.ca.
Lectures: MWF 15:00–15:50, Woodward 2.
Course webpage: http://www.math.ubc.ca/˜dghioca/courses/101.html
Course webpage for all Math 101 sections: http://www.math.ubc.ca/˜gerg
Office hours: Tu 11:45-13:15, Th 10:15-11:45.
Course outline: Section numbers below refer to the textbook; most of Chapters 5, 6, 7,
and 11 are covered, as well as parts of Chapters 8, and 9.
Week 1: Section 5.1: Areas and Distances and Section 5.2: The Definite Integral.
Week 2: Section 5.3: The Fundamental Theorem of Calculus, Section 5.4: Indefinite Integrals
and the Net Change Theorem (ignore sinh and cosh) and Section 5.5: The Substitution
Rule.
Week 3: Section 6.1: Areas Between Curves and Section 6.2: Volumes.
Week 4: Section 6.4: Work, Section 6.5: Average Value of a Function and Section 7.1: Integration by Parts (ignore ”reduction formulas”).
Week 5: Section 7.2: Trigonometric Integrals (ignore sin(mx) and cos(nx) for arbitrary, unspecified m and n) and Section 7.3: Trigonometric Substitution (ignore inverse secant and
inverse hyperbolic functions); Section 7.4: Integration of Rational Functions by Partial
Fractions (ignore the case iv of a repeated quadratic factor Q(x)).
Week 6: Section 7.7: Approximate Integration, and Section 7.8: Improper Integrals.
Week 7: Section 8.3: Applications to Physics and Engineering (ignore Hydrostatic Pressure,
Theorem of Pappus), and Section 9.3: Separable Equations (ignore Orthogonal Trajectories).
Week 8: Section 11.1: Sequences (ignore Definitions 2 and 5, Example 6, proof of Monotone
Sequence Theorem, Example 14), and Section 11.2: Series.
Week 9: Section 11.3 The Integral Test and Estimates of Sums (ignore Estimate the Sum and
Proof of the Integral Test), and Section 11.4: The Comparison Test.
Week 10: Section 11.5: Alternating Series Section; Section 11.6: Absolute Convergence and the
Ratio Test (ignore the Root Test).
Week 11: Section 11.8: Power Series, Section 11.9: Representations of functions as Power Series.
Week 12: Section 11.10: Taylor and Maclaurin Series (ignore Binomial Series).
Text: Calculus, Early Transcendentals, 7th edition by James Stewart. You may use an
older edition, but the suggested problems in the course will always be from the 7th edition.
Evaluation: The final mark will be based on Webwork (10%), two mid-terms (40%) and
the final exam (50%).
Midterms: Mid-terms will take place in class on Friday, January 30 and Friday, March
13.
Final Examination: This will be in the April examination period.
Policies: Missing a midterm or a Webwork assignment will normally result in a mark of
zero. Exceptions may be granted in two cases: prior consent of the instructor or a medical
emergency. In the latter case, the instructor must be notified as soon as possible (preferably
before the test), and presented with a doctor’s note immediately upon the student’s return
to UBC. When an exception is granted for a missed test, there is no special make-up test,
and the final exam mark will be used.
The Instructor reserves the right to change the present course outline at any
time during the semester.