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 2D
 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 Lâ€™Hospitalâ€™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 
       
3D 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 
MidExam  30 
EndExam  50 
Last Update: 03/02/2024

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