MATH*1080 - Elements of Calculus

Course Description

This course provides an introduction to the calculus of one variable with emphasis on mathematical modelling in the biological sciences. The topics covered include elementary functions, sequences and series, difference equations, differential calculus and integral calculus.

Learning Outcomes

1. Determine the domain, range and the inverse of a function and form a composite function;
2. Describe the differences between sequences and series, and use formulas resulting from finite and infinite series to solve problems involving payments, deposits, dosage of drugs, and population size;
3. Compute basic limits of functions and discuss the importance of limits to the process of differentiation. Determine where and whether functions are continuous, and identify and classify points of discontinuity;
4. Explain the derivative in terms of the idea of a tangent line to the graph of a function and how a derivative can be used to describe the rate of change of one quantity with respect to another;
5. Differentiate a wide class of single-variable functions, including polynomials, trigonometric, exponential, logarithmic, sums, products, quotients, compositions;
6. Apply the chain rule to find derivatives of different functions including functions raised to a power, exponential, and logarithmic functions;
7. Compute linear approximations to implicit functions using “implicit differentiation”;
8. Use derivatives to solve applied problems involving rate-of-change, maximum and minimum values; critical numbers; local extrema and concavity and optimization;
9. Use integrals to solve problems involving area;
10. Find a definite integral using the limit of Riemann sums;
11. Evaluate definite integrals using the Fundamental Theorem of Calculus; and
12. Find indefinite and definite integral using substitution.

Course Topics

• Preparing for Calculus
• Limits and Continuity
• The Derivative
• More About Derivatives
• Applications of the Derivative
• The Integral

Assessment