This course is designated for the students from IUP class, both from Computer Science and Chemistry of Faculty of Mathematics and Natural Sciences (FMNS), Universitas Gadjah Mada (2019/2020).
All the information here can be obtained in Modul handbook of Undergraduate Program of Mathematics.
Course Outcome
After completing this course the students should have:
| CO1. | ability to understand the fundamental concepts of one variable calculus such as functions, limit, derivative, differential,and its geometry interpretation |
| CO2. | ability to solve the standard problems on calculus such as properties on real numbers, functions, limit, and derivative. |
| CO3. | ability to apply the concepts of calculus to solve problems in mathematics and sciences especially related to optimization problems. |
| CO4. | ability to use limit and derivative to obtain the information about a function such as increasing or decreasing, concavity, extreme points, inflection points, including sketching its graph. |
| CO5. | ability to determine the Taylor series and MacLaurin series of a function. |
Content
The course will cover about the system of real numbers, functions and their graph, the limit of a function, continuity, the derivative, the geometric interpretation of the derivative, higher-order derivatives, the Mean Value Theorem, L’Hospital’s rule theorem of extreme value, applications of extreme problem,increasing and decreasing functions, concavity, inflection points, sketching the graph of functions, Taylor and MacLaurin series.
Reading List
- James Stewart, 2015, Calculus: Early Transcendentals Single Variable 8th Ed., Willey, USA
- Robert A. Adam and Christopher Essex, 2010, Calculus, A Complete Course, Pearson.
- James Stewart, 1999, Calculus, 4th edition, Brooks/Cole Pub. Comp.
- Abe Mizrahi and Michael Sullivan, 1990, Calculus and Analytic Geometry, Wadsworth.
- Tim Pengajar Kalkulus, Diktat Kuliah Kalkulus I, FMIPA UGM.