| Course Type | Compulsory Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | 1 |
|---|
| Semester | First Term (Fall) |
|---|
| ECTS | 6 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- It is equipped with the necessary Engineering Mathematics knowledge in specific areas of engineering disciplines.
- Gain analytical thinking ability.
- Problem solving skills develop.
- They can apply mathematical knowledge to engineering problems.
|
| Mode of Delivery | Face to face |
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| Prerequisites | No |
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| Recommended Optional Programme Components | None |
|---|
| Course Description | This is a First Course in Freshman Calculus. Its content comprises of the following concepts: Functions, Limit and Continuity. The derivative and its Applications, Indefinite and Definite Integrals. Trigonometric, Logarithmic, Exponential and Hyperbolic Functions and their Inverses. Techniques of Integration. Applications of the Definite Integral: Area, Volume and Arclength. Indetermined Forms, L' Hopital's Rule. Improper Integral. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Functions & Their Graphs: Rational Functions, Trigonometric Functions, Exponential Functions, Inverse Functions. |
|
2nd Week |
Logarithmic and Inverse Trigonometric Functions. Limits & Continuity: Limits, One-Sided Limits, Limits Involving Infinity. |
|
3rd Week |
Asymptotes. Continuity. The Intermediate Value Theorem. |
|
4th Week |
Derivatives. Rules of Differentiation. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. |
|
5th Week |
Related Rates. Derivatives of Inverse Functions. Logarithmic Differentiation. |
|
6th Week |
Applications of Derivatives. Sketching the Graphs of Functions. |
|
7th Week |
The Mean Value Theorem. L'Hopital's Rule. Review. |
|
8th Week |
Midterm Exam |
|
9th Week |
Optimization, Integration: Indefinite Integrals. Integration by Substitution. |
|
10th Week |
Definite Integrals, The Mean Value & Fundamental Theorems. |
|
11th Week |
Substitution in Definite Integrals. Area Problems. |
|
12th Week |
Applications of Integrals: Volume by Slicing & Cylindrical Shells. Lengths of Plane Curves. |
|
13th Week |
Integration Techniques: Integration by Parts, Trigonometric Substitutions, Partial Fractions. |
|
14th Week |
Improper Integrals, Short Exam. |
|
15th Week |
Review. |
|
| Recommended or Required Reading | Weir MD, Hass J, Giordano FR (2005) Thomas' Calculus, 11th Ed., Addison-Wesley.
Adams, R.A., Calculus (2003), 4th Ed., Addison-Wesley.
Swokowski, E.W., Olinick, M., Pence, D., Calculus (1994), 6th Ed., PWS Publishing Company.
|
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
35 |
| Quiz |
2 |
15 |
| Total(%) |
|
50 |
| Contribution of In-term Studies to Overall Grade(%) |
|
50 |
| Contribution of Final Examination to Overall Grade(%) |
|
50 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
10 |
2 |
20 |
| Individual or group work |
7 |
2 |
14 |
| Preparation for Final exam |
1 |
40 |
40 |
| Course hours |
14 |
5 |
70 |
| Preparation for Midterm exam |
1 |
30 |
30 |
| Laboratory (including preparation) |
0 |
0 |
0 |
| Final exam |
1 |
2 |
2 |
| Homework |
0 |
0 |
0 |
| Quiz |
2 |
1 |
2 |
| Total Work Load | 180 |
| Total Work Load / 30 (h) | 6 |
| ECTS Credit of the Course | 6 |
|
| Language of Instruction | English |
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| Work Placement(s) | No |
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