Calculus I

3.7 SMA 3112 CALCULUS I

3.7.1 Purpose
To equip the learner with techniques of differentiation and their applications in Science, Engineering and Technology.

3.7.2 Expected Learning Outcomes
At the end of this course, the learner should be able to;
1. Define a function
2. Use basic principles of differentiation to find derivatives of simple functions.
3. Distinguish between parametric and implicit differentiation.
4. Find higher order derivatives.
5. Apply the techniques of differentiation in problem solving.

3.7.3 Course content
Limits: polynomial, rational and simple trigonometric functions. Continuity and differentiability of functions, graphical illustration of continuity. Differentiation by first principles and by rule for x n (integral and fractional n), sums, products, quotients, chain rule, trigonometric, logarithmic and exponential functions of a single variable. Differentiation of Hyperbolic functions. Implicit and Parametric differentiation. Second and higher order derivatives. Applications such as equations of tangent and normal, kinematics, rates of change, stationary points and economics and financial models.

3.7.6 Course Assessment
Continuous Assessment Tests 30%
Written end of semester examination 70%
Total marks 100%

3.7.7 Core References
1. Hoffmann, L., & Bradley, G. (2010). Applied calculus for business, economics, and the social and life sciences. New York, NY: McGraw-Hill.
2. Larson, R., & Edwards, B. (2010). Calculus. Belmont, Calif.: Brooks/Cole, Cengage Learning.

3.7.8 Recommended References
1. Weir, M., Hass, J., Giordano, F., & Thomas, G. (2008). Thomas' calculus. Boston, Mass.: Pearson Addison Wesley.
2. Hass, J., Weir, M., & Thomas, G. (2009). University calculus. Boston: Pearson/Addison Wesley.