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Accelerated Calculus II
| Course Code | Semester |
Course Name |
LE/RC/LA |
Course Type |
Language of Instruction |
ECTS |
| MCB1011 |
1 |
Accelerated Calculus II |
4/2/0 |
TBD |
English |
7 |
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| Course Goals |
To teach the fundamental mathematical concepts to be used in engineering problems. |
| Prerequisite(s) |
None |
| Corequisite(s) |
None |
| Special Requisite(s) |
None |
| Instructor(s) |
Professor Emel Yavuz |
| Course Assistant(s) |
None |
| Schedule |
Monday 11:00-13:00 - B1-3; Tuesday 11:00-13:00 - B1-2; Wednesday 13:00 - ZB-2 |
| Office Hour(s) |
Emel Yavuz, 3A-1, Tuesday 13:00-15:00 |
| Teaching Methods and Techniques |
Lectures and Recitations |
| Principle Sources |
Robert A. Adams and Christopher Essex. Calculus: A complete course, 8th edition, Pearson Publ., 2013. |
| Other Sources |
Weir and Hass, Thomas' Calculus, Thirteen Edition, 2016, Pearson Publication. |
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| Course Schedules |
| Week |
Contents |
Learning Methods |
| 1. Week |
5.1 Sums and Sigma Notation
5.2 Areas as limits of Sums |
Lectures and Recitations |
| 2. Week |
5.3 The Definite Integral
5.4 Properties of the Definite Integral |
Lectures and Recitations |
| 3. Week |
5.5 The Fundamental Theorem of Calculus
5.6 The Method of Substitution |
Lectures and Recitations |
| 4. Week |
5.7 Areas of Plane Regions
6.1 Integration by Parts |
Lectures and Recitations |
| 5. Week |
6.2 Integration of Rational Functions |
Lectures and Recitations |
| 6. Week |
6.3 Inverse Substitutions |
Lectures and Recitations |
| 7. Week |
6.5 Improper Integrals |
Lectures and Recitations |
| 8. Week |
7.1 Volumes by Slicing-Solids of Revolution
7.3 Arc Length and Surface Area |
Lectures and Recitations |
| 9. Week |
8.2 Parametric Curves
8.4 Arc Lengths and Areas for Parametric Curves |
Lectures and Recitations |
| 10. Week |
8.5 Polar Coordinates and Polar Curves
8.6 Slopes, Areas, and Arc Lengths for Polar Curves |
Lectures and Recitations |
| 11. Week |
9.1 Sequences and Convergence
9.2 Infinite Series |
Lectures and Recitations |
| 12. Week |
9.3 Convergence Tests for Positive Series |
Lectures and Recitations |
| 13. Week |
9.4 Absolute and Conditional Convergence |
Lectures and Recitations |
| 14. Week |
9.5 Power Series
9.6 Taylor and Maclaurin Series |
Lectures and Recitations |
| 15. Week |
Final Exam Week |
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| 16. Week |
Final Exam Week |
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| 17. Week |
Final Exam Week |
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| Assessments |
| Evaluation tools |
Quantity |
Weight(%) |
| Midterm(s) |
1 |
40 |
| Quizzes |
10 |
20 |
| Final Exam |
1 |
40 |
| Program Outcomes |
| PO-1 | Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science. | | PO-2 | Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science. | | PO-3 | Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence. | | PO-4 | Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline. | | PO-5 | Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science. | | PO-6 | Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish. | | PO-7 | Using time effectively in inventing solutions by implementing analytical thinking. | | PO-8 | Understanding professional ethics and responsibilities. | | PO-9 | Having the ability to behave independently, to take initiative, and to be creative. | | PO-10 | Understanding the importance of lifelong learning and developing professional skills continuously. | | PO-11 | Using professional knowledge for the benefit of the society. | |
| Learning Outcomes |
| LO-1 | Discuss and explain antiderivatives, the indefinite integral, sums and sigma notation, and areas as limits of sums | | LO-2 | Identify the definite integral and properties of it | | LO-3 | Describe the Fundamental Theorem of Calculus, the method of substitution, and integration by parts | | LO-4 | Explain integrals of rational functions and inverse substitutions | | LO-5 | Identify areas of plane regions | | LO-6 | Express improper integrals | | LO-7 | Identify volumes by slicing and Solids of revolution; discuss the arc length and surface area | | LO-8 | Explain parametric curves, smooth parametric curves and their slopes, and arc lengths and areas for parametric curves | | LO-9 | Analyze polar coordinates and polar curves | | LO-10 | Identify slopes, areas, and arc lengths for polar curves | | LO-11 | Describe sequences and convergence | | LO-12 | Analyze infinite series, convergence tests for positive Series, and absolute and conditional convergence | | LO-13 | Explain and discuss power series, and Taylor and Maclaurin series | |
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| Course Assessment Matrix: |
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| | PO 1 | PO 2 | PO 3 | PO 4 | PO 5 | PO 6 | PO 7 | PO 8 | PO 9 | PO 10 | PO 11 | | LO 1 | | | | | | | | | | | | | LO 2 | | | | | | | | | | | | | LO 3 | | | | | | | | | | | | | LO 4 | | | | | | | | | | | | | LO 5 | | | | | | | | | | | | | LO 6 | | | | | | | | | | | | | LO 7 | | | | | | | | | | | | | LO 8 | | | | | | | | | | | | | LO 9 | | | | | | | | | | | | | LO 10 | | | | | | | | | | | | | LO 11 | | | | | | | | | | | | | LO 12 | | | | | | | | | | | | | LO 13 | | | | | | | | | | | |
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