Limits, continuity and differentiation of functions of one variable; differentials and linear approximations; applications of differentiation to related rates, optimization, and curve sketching. Further topics include selected integration, Taylor and Maclaurin series, partial differentiation and its applications to linear approximation and optimization.
Date First Offered:
Total Hours: 90
Lecture Hours: 70
Laboratory Hours: 20
This course is offered online:
MATH 100 Technical Mathematics for Geomatics
- Functions and Models
- Limits and Rates of Change
- Inverse Functions
- Applications of Differentiation
- Partial Derivatives
- Applications of Partial Derivatives
- Taylor and Maclaurin Series
Upon successful completion of the course, a student will be able to:
1. Use the definition and laws of the limit to evaluate the limits of functions.
2. Evaluate the derivatives of elementary functions built from constant functions, power functions, exponential functions, logarithmic functions, trigonometric functions, and inverse trigonometric functions using the properties of differentiation, particularly the Product Rule, the Quotient rule, and the Chain Rule.
3. Carry out implicit differentiation.
4. Solve related rates problems.
5. Solve optimization problems.
6. Use properties of functions such as monotonicity, extrema, and points of inflection to aid curve-sketching.
7. Use linearization and differentials to approximate values of functions.
8. Evaluate indefinite integrals with basic properties and the Substitution Rule.
9. Evaluate definite integrals with the Fundamental Theorem of Calculus and the Substitution Rule.
10. Set up and evaluate the definite integrals for the areas of plane regions.
11. Evaluate partial derivatives of functions of several variables.
12. Use partial derivatives to find the critical points.
13. Use the Second Derivative Test to determine the natures of critical points.
14. Use the method of Lagrange multipliers to solve simple optimization problems.
15. Carry out the Taylor and Maclaurin series expansion of functions of one or two variables.
16. Use the Taylor series expansion to approximate the values of functions.
Final Exam: 45 %
Midterm Exam: 40 %
Quizzes and Tests: 15 %
Percentage of Individual Work:
Course Offered in Other Programs:
Required - Stewart, J., 2008, Single Variable Calculus, 6th Edition (Brooks/Cole). Chapters Covered: 1-5
Required - Cui, H., Supplementary Materials