Coordinating Unit: Department of Mathematics, Faculty of Science and Technology
Supporting Unit(s): Nil
Course Code: MATH1003 Year of Study: 1
Course Title: Intermediate Calculus
Compulsory/Elective: Compulsory
Course Prerequisites: GEST1004 Quantitative Reasoning for Science and Technology
Prerequisite Knowledge: Nil
Duration: One semester Credit Units: 3
Class/Laboratory Schedule: Three hours of lecture and one hours of tutorial per week.
Laboratory/Software Usage: Nil
Course Description: This course is a continuation of the course Quantitative Reasoning for Science and Technology. The topics include methods of integration, parametric curves, sequence and series, vectors and curves in space. The two courses together aim at providing students with a solid foundation of one variable calculus.
Course Objectives: 1.         To introduce more methods of integration, and parametric curves

2.         To introduce sequence and series

3.         To introduce vectors and curves in space
Learning Outcomes (LOs): Upon completion of this course, students are expected to:

1.      Be able to find integrals using various methods.

2.      Be able to do computations with parametric curves.

3.      Be able to identify and use infinite series.

4.      Be able to solve problems with vectors and curves in space.
Texts & References:

 

(* recommended textbook(s))

 1.         *Calculus, Early Transcendentals Version, 7th Ed, C. H. Edwards and D. E. Penney, Prentice Hall.

2.         Calculus and analytical geometry, 9th Ed. Thomas and Finney, Addison Wesley.
Student Assessment: •        Assignments: 15%

•        Midterm examination: 25%

•        Final examination: 60%
Learning Outcome Assessment: •     Assignments, midterm and final examination

 

Course Content: (topic outline)  

Week no. Topics Assignment no. LO no.
1-3 Techniques of integration

Substitution, integration by parts, trigonometric integrals, partial fractions, trigonometric substitution, improper integral

 1 – 3 1
4, 5 Polar coordinate and parametric curves

Area computation in polar coordinates, parametric curves, integral computations with parametric curves

 4, 5 2
6, 7 Infinite sequence

Convergence of sequence, operations of limit of sequences

 6 3
7 Midterm examination
8-12 Infinite series

Infinite series and convergence, Taylor series and Taylor polynomials, integral test, comparison test, alternating series and absolute convergence, power series 

7-10 3
13-15 Vectors, curves and surface in space

Vectors in plane and space, cross product, lines and planes, curves and motion in space, curvature and acceleration, cylinder and quadric surfaces, cylindrical and spherical coordinates

 11 – 13 4
TBA Final Examination