MAT1203: Calculus III

This is an advanced calculus course covering topics needed for analysis in physical, life and social science disciplines.  The topics covered include: Preliminary Concepts on Vectors and Quadratic Surfaces; Functions of Several Variables; Multiple Integrals; Topics in Vector Calculus; and Classical Theorems and Applications.

Course Objectives 
By the end of the course the student should be able to: 

• State the basic notations and concepts of vectors in 3-dimension R3, cylinders and quadratic surfaces, cylindrical and spherical coordinates, vector functions. 
• Demonstrate the domain and graphic surfaces for functions of two or more variables, apply the concepts of limit and continuity in analysis of function of two or more variables, and appreciate from first principles the concept of partial derivatives and their application to limits and continuity, directional derivatives, linearity, maxima and minima as well as the Lagrange multiplier.  
• Generate the concept multiple integrals using the Principle Riemann integral and Jordan Measure and apply such concepts in evaluating the volumes under a given surface domain, surface areas, change of variable in multiple integrals, and Jacobean transformation. 
• Analyze the concept of vector field in regard to gradient fields and conservative vector field, and apply such to line integrals, generate the fundamental theorem of line integrals, investigate the independence of path in open, not open, connected and not connected regions.    
• Derive the concept of Green’s theorem and its applications to finding area, the curl and divergence of a vector field, and the Green theorem in vector field. Appreciate the concepts of Classical Theorems as regards the oriented and non oriented surfaces, Classical Green’s theorem, and surfaces integrals of vector fields, Stokes Theorem and its applications to divergence theorem. 

Expected Learning Outcomes 

• To discuss the basic competence in the concepts, principles, and procedures of mathematical analysis functions of several variables with application to general theory of geometric differentiation and integration and the use of a graphing calculator technology, when appropriate. 
• To encourage orderliness, speed and accuracy in the presentation of advanced mathematics. 
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly. 
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills. 
• To build a strong foundation in calculus as preparation for subsequent courses in mathematics and other sciences.