Lecture: 4 hours/week
and
Tutorial: 1 hour/week
Classroom time will be used for:
- Lectures
- Demonstrations
- Discussions
- Problem-solving practice
- In-class assignments (which may include work in groups).
Definite and Indefinite Integrals
- Definition of the Riemann integral
- The Fundamental Theorem of Calculus
- Antiderivatives and indefinite integrals
- The Net Change Theorem
Techniques of Integration
- The substitution rule
- Integration by parts
- Trigonometric integrals
- Trigonometric substitution
- Partial fraction decomposition of rational functions
- Numerical approximation methods for integrals: Midpoint Rule, Trapezoidal Rule, Simpson's Rule
- Rationalizing substitutions
- Improper integrals
Applications of Integration
- Area between curves
- Volumes by cross-sections and cylindrical shells
- Length of a curve
- Separable differential equations work
Parametric Equations and Polar Coordinates
- Length of curves in parametric form
- Area of curves in polar coordinates
Sequences and Series
- Cnvergence/divergence of sequences
- convergence/divergence of sequences of partial sums
- sums of infinite geometric series
- the harmonic series
- properties of convergent series
- Integral test
- Comparison tests
- Alternating series test
- Absolute and conditional convergence
- Ratio and root tests
Power Series
- Intervals and radii of convergence
- Representation of functions as power series
- Differentiation and integration of power series
- Taylor and Maclaurin series
- Applications of Taylor Polynomials
Upon successful completion of the course, students will be able to:
- Compute finite Riemann sums;
- Form limits of Riemann sums and write the corresponding definite integral for a given function;
- Apply the Fundamental Theorem of Calculus to evaluate integrals using basic antiderivatives and techniques of integration;
- Choose an appropriate integration method to find antiderivatives and evaluate definite integrals;
- Approximate the value of a definite integral using numerical approximation methods, including the Midpoint Rule, Trapezoidal Rule and Simpson's Rule;
- Apply integration techniques to solve problems related to areas, volumes, arc length, position, velocity, acceleration and work;
- Solve simple separable differential equations;
- Determine the convergence or divergence of improper integrals;
- Determine convergence/divergence properties of a given sequence or series;
- Represent a given function as a power series;
- Find the Taylor series representation of a given function;
- Approximate a differentiable function by a Taylor polynomial and compute the error that results from using the approximation;
- Determine the radius and interval of convergence of a power series;
- Find the area of a region bounded by the graph of a polar equation;
- Find the length of a curve given in Cartesian form or parametric form.
Assessment will be in accordance with the °µÍø51 Evaluation Policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Evaluation will be based on the following:
| Quizzes | 0-20% |
| Test(s) | 20-70% |
| Assignments | 0-15% |
| Attendance | 0-5% |
| Class participation | 0-5% |
| Tutorials | 0-10% |
| Final examination |
30-40% |
| Total |
100% |
Instructors may use a student’s record of attendance and/or level of active participation in the course as part of the student’s graded performance. Where this occurs, expectations and grade calculations regarding class attendance and participation will be clearly defined in the Instructor’s Course Outline.
Consult the °µÍø51 Bookstore for the current textbook. Examples of textbooks may include:
Stewart. (Current Edition). Calculus: Early Transcendentals. Cengage Learning.
Anton, Bivens, and Davis. (Current Edition). Calculus: Early Transcendentals. Wiley.
Briggs, Cochran, and Gillet. (Current Edition). Calculus: Early Transcendentals. Pearson.
Edwards and Penney. (Current Edition). Calculus: Early Transcendentals. Pearson.
Feldman, Joel; Rechnitzer, Andrew and Yeager, Elyse. (2024). CLP-2 Integral Calculus. UBC.
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