Amirah Hana Mohamed Nor
SYLLABUS MAT183 (CALCULUS 1) pg. 1 Amirah 2023 ________________________________________________________________________________ COURSE : CALCULUS I COURSE CODE : MAT183 PROGRAMME : Diploma in Civil Engineering (EC110 - Part 1) Diploma in Science (AS120 - Part 2) Diploma in Computer Science (CS110 - Part 2) LECTURER : PN. AMIRAH HANA HJ. MOHAMED NOR ROOM : L2- 72 PHONE : 09-460 2429 (Off), 019-920 1003 (H/P) ________________________________________________________________________________ SYNOPSIS This is the first course in the calculus series. It starts with topics on functions and graphs, limit and continuity, techniques of differentiation and its applications. It also covers simple integration and its applications. COURSE LEARNING OUTCOMES At the end of the course, students should be able to: 1. Apply the properties of function, limit and continuity, techniques of differentiation and integration. (PLO1, C3) 2. Analyse appropriate graph of polynomial or rational function in solving related mathematical problems using calculus. (PLO6, C4) 3. Demonstrate active collaboration with team members in identify problems related to lifelong learning that involve with application in differentiation and integration. (PLO7, A3) TEACHING METHOD • Lecture • tutorial • laboratory • (Plus YouTube Channel, Telegram Group, Google Classroom) UNIVERSITI TEKNOLOGI MARA PAHANG
SYLLABUS MAT183 (CALCULUS 1) pg. 2 Amirah 2023 ASSESSMENT
SYLLABUS MAT183 (CALCULUS 1) pg. 3 Amirah 2023 SYLLABUS CONTENTS CHAPTER TOPIC NOTES 1 LIMITS AND CONTINUITY (Week 1, 2, 3) • Functions • Operations on functions • Graphs of functions • Limits (an intuitive introduction and computational approach) • Continuity • Limits and continuity of trigonometric functions 2 DIFFERENTIATON (Week 4, 5, 6) • Differentiation using the first principle Tangent lines and rates of change • The derivatives • Techniques of differentiation • Derivatives of trigonometric functions • The chain rule • Implicit differentiation • Higher order derivatives • Linear Approximation and Differentials After week 5 : MID TERM BREAK (1 week) 24/04/2023 – 30/04/2023 ASSESSMENT 1 (Test 30%) (90 minutes) Week 6 3 APPLICATIONS OF DIFFERENTIATION (Week 7, 8, 9) • dx dy as a gradient/slope of tangent line • Intervals of increase and decrease • Concavity • First and second derivatives tests • Graphs of polynomial functions; asymptotes • Maximum and minimum values of function • Applied maximum and minimum problems • Related rates • Rolle’s Theorem • Mean-Value Theorem for differentiation ASSESSMENT 2 (MAPLE 10%) (1 week) Week 9 After week 9 : CUTI RAYA PUASA (1 week) 29/05/2023 – 2/06/2023 4 INTEGRATION (Week 10, 11, 12) • Introduction • The idea of indefinite & definite integrals • Basic integration formulas (constant rule, power rule, sum & difference rules, trigonometric rule, exponential rule, logarithmic rule) • Integration by u-substitution (power rule, trigonometric rule, exponential rule, logarithmic rule, powers of sine & cosine) • Sigma notation and the Riemann Sums • Mean-Value Theorem for integral • Second fundamental theorems of Calculus ASSESSMENT 3 (Video Presentation 10%) (3 weeks) Week 11 After week 12 : CUTI RAYA PUASA (1 week) 26/06/2023 – 2/07/2023 5 APPLICATIONS OF THE DEFINITE INTEGRAL (Week 13, 14) • Area between two curves • Volumes of revolution : o Volume by Disks o Volume by Washer o Volume by Shell ASSESSMENT 4 (Final Examination 50%) (3 hours) ALL CHAPTERS Week 15 @ 16
SYLLABUS MAT183 (CALCULUS 1) pg. 4 Amirah 2023 REFERENCES 1. H. Anton, Calculus 10th edition, John Wiley & Sons, Inc., 2012 2. Finney, Weir and Giordano, Thomas, Calculus, 10th edition, Addison-Wesley Pub. Com., 2001 3. James Stewart, Calculus, 5th edition, Brooks/Cole Pub. Com., 1999 4. G. L. Bradley and K.L. Smith, Calculus, 2nd edition, Prentice-Hall Inc., 1000 5. D.Varberg and E.J. Purcell, Calculus, 7th edition, Simon and Schuster (Asia) Pte. Ltd., 1997 6. Edwards and Penney, Calculus With Analytic Geometry, 5th edition, Prentice Hall International Inc., 1998 7. Nazirah Ramli, Salimah Ahmad and Amirah Hana Mohamed Nor, Introduction to Calculus for Science and Engineering Students, Venton Publishing (M) Sdn. Bhd., 2016