GP115 Calculas I

Course Code
GP115
Course Title
Calculas I
Credits
3
Course Type
CORE
Intended Learning Outcomes (ILOs)
Knowledge:
At the end of this course, a student will be able to;
  • Analyze conceptual problems in limits, continuity, differentiability, and integration of functions of single variables and compute the partial derivatives of functions of several variables.
Skill:
At the end of this course, a student will be able to;
  • Compute the roots of unity, the derivatives of complex functions, and identify Holomorphic functions
  • Identify and sketch conic sections, use polar and other coordinates to represent points in 2-D
  • Compute the vector and cartesian equations of lines and planes, the derivatives of vector valued functions, and solve related problems
Attitude:
  • Determine the convergence of sequences and infinite series, calculate the radius of convergence and interval of convergence of power series and find the power series expansion of analytic functions
Textbooks and References
  • James Stewart (2006). Calculus (Fifth Edition), Thomson Books/Cole
  • Watson Fulks (1978). Advanced Calculus an Introduction to Analysis (3rd Edition) John Wiley & sons, Inc.
  • H.K. Dass(2008). Advanced Engineering Mathematics
  • Lecture notes and handouts
Topic Time Allocated / hours
L T P A
Review
Sets and their applications, Real number system and its properties, Method of mathematical induction, Concept of a function, Description and classification of functions 		- - - -
Functions of a Single Variable
Limits, Indeterminate forms and L’Hospital’s rule, Continuity and Differentiability of real valued functions 		- - - -
Applications
Intermediate value theorem, mean value theorem, Leibnitz theorem, and tangent line approximation 		- - - -
Sketching curves
Local and global maximum and minimum, inflection points 		- - - -
Applications of Integration
Identify Reimann definition and find arc lengths, areas, volumes and moments using integration 		- - - -
Function of Several Variables
Partial derivatives and total differential, Chain rule and higher order partial derivatives 		- - - -
Parametric representation of curves in planes, Curvature, radius and centre of curvature
- 		- - - -
Complex functions
Roots of unity and functions of complex variables, Mapping of complex variables, Derivatives of complex functions, Cauchy Reimann equation, Holomorphic functions 		- - - -
3-D Coordinate Geometry
Vector equations of lines and planes in space, Coplanar lines, Shortest distance between a point (line, plane) and a line (plane), Skew lines in the space, Angels between planes and the equation of the intersection line, Derivatives of vector valued function 		- - - -
Function of positive integers
Define sequences and examples, Monotonic sequence and bounded sequence, Convergence, divergence and oscillation of a sequence 		- - - -
Infinite Series
Standard examples of infinite series, conditions for convergence, Alternating series, Absolute and conditional convergence 		- - - -
Real Power Series
Power series of function f(x); Binomial expansion, Radius and interval of convergence of power series, Maclaurin and Taylor series approximation 		- - - -
Total (hours)
36 - - 18

L = Lectures, T = Tutorial classes, P = Practical classes, A = Homework Assignments

Assessment Percentage Marks
Assignments 20
Mid-Exam 30
End-Exam 50
Last Update: 03/02/2024 | Edit this page