| Calculus & Analytical Geometry Course Code: GEDU-202 | |||||
|---|---|---|---|---|---|
| Credit Hours: | 3 (3+0) | Prerequisites: | NIL | ||
| Course Learning Outcomes (CLOs): | |||||
| At the end of the course the students will be able to: | Domain | BT Level* | |||
| Define and explain the ideas of differential and integral calculus | C | 1 | |||
| Using derivatives to solve application problems involving rates of change and integration to solve application problems involving areas between curves. | C | 2,3 | |||
| Use vector calculus and analytical geometry in multiple dimensions. | C | 3 | |||
| BT= Bloom’s Taxonomy, C=Cognitive domain, P=Psychomotor domain, A=Affective domain | |||||
| Course Contents |
| Functions: Definition, real life examples, domain and range of functions, arithmetic of functions, composite functions. Functions: Piecewise defined functions, Graph of functions, shifting of graphs, even and odd functions, real life application Limits: Rate of change, Limits of function values, Limit of Piecewise functions, Power and Algebraic rules of limits, Algebraic elimination of zero denominators. Limits: Sandwich theorem, left hand limit and right hand limit, Intermediate forms of limits, infinite limits Tutorial. Continuity: Continuity at a point, continuity tests, continuous functions, Properties of continuous functions, Examples of discontinuous functions. Continuity: Intermediate value theorem for continuous functions, limits at infinity (and of rational functions), Infinite limits and asymptotic behavior of functions Tutorial. Derivatives: Motivation, Derivative at a point and tangent line (also normal line), the derivative of a function, rules of differentiation, derivatives of algebraic, trigonometric and exponential functions. Derivatives More complex and implicit differentiation, chain rule, linearization and differentials Tutorial. Application of Derivatives: Use of first derivative for finding local maxima and minima, use of second derivative for finding concave up and concave down functions graphs, extreme values of functions. Application of Derivatives: Curve sketching, the mean value theorem Tutorial. Integration/Anti-derivatives: Estimation of area under the curve using finite sum, sigma notation and limit of finite sums, techniques of integration. Integration/Anti-derivatives: The definite integral and its application, application of integration: area under the curve. Integration/Anti-derivatives: Improper integral, Tutorial.Analytical Geometry: Different forms of equations of line in two-dimensional plane 𝑅2 , drawing, finding their intersections.Analytical Geometry Different forms of equations of lines and planes in three-dimensional space 𝑅3 , drawing, finding their intersections. |
| Teaching Methodology |
| Lectures, Written Assignments, Practical labs, Semester Project, Presentations |
| Text Book |
| Thomas Calculus (14 edition). |
| Reference Materials |
| Calculus and Analytic Geometry by Kenneth W. Thomas. Calculus by Stewart, James. Calculus by Earl William Swokowski; Michael Olinick; Dennis Pence; Jeffery A.Cole. |