Limits, compound interest, continuity. Derivative and rules of differentiation. Exponential and logarithmic functions. Extremal values, trends, elasticity of demands. Linear programming and multiple optimum solutions. Simplex method and optimization. Applications to compound interest, present value, annuities, amortization of loans. Applications to modeling in economics and business. Introduction to probability and statistics.
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Teaching Methods | Assessment Methods |
| 1) Learns the foundational notions of Calculus: limit and continuity. | 1 | A |
| 2) Learns the notion of derivative through limit, learns properties of derivation and the chain rule. | 1 | A |
| 3) Learns implicit differentiation. | 1 | A |
| 4) Learns sketching of curves in cartesian coordinates, can do extremum calculations. Learns the notion of concavity. Learns: 1st derivative test, 2nd derivative test and the applications of the notions maxima and minima | 1 | A |
| 5) Solves compound interest questions and learns the notion of present value. | 1 | A |
| 6) Learns basic counting techniques and can do elemantary probability and statistical calculations. | 1 | A |
Course Flow
| Week | Topics | Study Materials |
| 1 |
Chapter 10: Limit and Continuity
Limits |
10.1, 10.2 |
| 2 | Continuity | 10.3 |
| 3 |
Chapter 11: Differentiation
The Derivative, Rules of Differentiation |
11.1, 11.2 |
| 4 | The product rule and the Quetient rule, The chain rule | 11.4, 11.5 |
| 5 |
Chapter 4: Exponential and Logarithmic Functions
Exponential Functions, Logarithmic Functions |
4.1, 4.2 |
| 6 | Properties of Logarithms, Logarithmic and Exponential Equations | 4.3, 4.4 |
| 7 |
Chapter 12: Additional Differentiation Topics
Derivative of logarithmic functions, Derivatives of Exponential Functions |
12.1, 12.2 |
| 8 | Implicit Differentiation, Logarithmic Differentiation | 12.4, 12.5 |
| 9 |
Chapter 13: Curve Sketching
Relative Extreme Absolute Extrema on Closed Interval, Concavity |
13.1, 13.2, 13.3 |
| 10 | The Second Derivative Test, Asymptotes, Applied Maxima and Minima | 13.4, 13.5, 13.6 |
| 11 |
Chapter 5: Mathematics of Finance
Compound Interest, Present Value |
5.1, 5.2, 5.4 |
| 12 | Interest Compounded Continuously |
5.3
|
| 13 |
Chapter 8: Introduction to Probability and Statistics
Basic Counting Principle and Permutations, Combinations and Other Counting Principles |
8.1, 8.2 |
| 14 | Sample Spaces and Events, Probability | 8.3, 8.4 |
Recommended Sources
| Textbook |
Introductory Mathematical
Analysis, 13th Edition by Ernest Haeussler, Richard S. Paul, Richard Wood, Pearson Prentice Hall |
| Additional Resources |
Material Sharing
| Documents | |
| Assignments | |
| Exams |
Assessment
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 1 | 100 |
| Quizzes | ||
| Assignments | ||
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 60 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 40 | |
| Total | 100 |
| COURSE CATEGORY |
Course’s Contribution to Program
| No | Program Learning Outcomes | Contribution | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | ||||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | ||||||
| 3 | Ability form and interpret the relations between research topics in mathematics | ||||||
| 4 | Ability to define, formulate and solve mathmatical problems | ||||||
| 5 | Consciousness of professional ethics and responsibilty | ||||||
| 6 | Ability to communicate actively | ||||||
| 7 | Ability of self-development in fields of interest | ||||||
| 8 | Ability to learn, choose and use necessary information technologies | ||||||
| 9 | Lifelong education | ||||||
ECTS
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 3 | 42 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 4 | 56 |
| Mid-terms (Including self study) | 1 | 12 | 12 |
| Final examination (Including self study) | 1 | 15 | 15 |
| Total Work Load | 125 | ||
| Total Work Load / 25 (h) | 5 | ||
| ECTS Credit of the Course | 5 |