Academics Links
Calculus and Analytical Geometry (MTCE1013)
Prerequisite(s)
None
Recommended Book(s)
Calculus And Analytic Geometry, Addison Wesley, 9th Edition
Reference Book(s)
Calculus, Schum’s Series, Latest Edition
Calculus And Analytic Geometry, H.Antom, Latest Edition
Course Objectives
1. To learn fundamentals of mathematics, calculus and analytical geometry. 2. To enable students to apply the ideas to solve problems of practical nature.
Course Learning Outcomes (CLO)
CLO:1 Have knowledge related to the fundamentals of calculus and analytical geometry. CLO:2 Understand the differentiation integration and their applications. CLO:3 Apply the acquired knowledge to solve problems of practical nature. 
Course Contents
Complex Numbers

Basic operations

Graphical representations

Polar and exponential forms of complex numbers

De’moivre’s theorem with applications
Functions

Hyperbolic functions and their graphical representation

Hyperbolic and trigonometric identities and their relationship

Exponential functions
Differentiation

Differentiation and successive differentiation and its application to rate, speed and acceleration

Leibritze’s theorem and its applications

Equations of tangents and normals, curvature

Radius and centre of curvature

Maxima and minima of function of one variable and its applications

Convexity and concavity

Points of inflexion

Concept of infinite series

Taylor’s and mclaurin’s series and expansion of functions

Errors and approximations and limiting values of functions
Partial Differentiation

Partial differential coefficient and chain rule

Partial differentiation of an implicit function

Total differential

Euler’s theorem

Applications to small errors and approximations

Statement of taylor’s theorem of two independent variable and its applications
Integral Calculus

Standard integrals

Function of a linear function

Integration by substitution, by partial fractions and by parts

Integration of trigonometric functions

Definite integrals and their properties and reduction formulae

Curve tracing in rectangular and polar coordinates
Integration Applications

Volumes of solids of revolution

Centroid of a plane figure

Centre of gravity of a solid of revolution

Lengths of curves

Surface revolution

Rules of pappus

Moment of inertia

Radius of gyration

Parallel axes theorem

Perpendicular axes theorem

Second moment of area

Composite figures

Centres of pressure and depth of centre of pressure
Analytical Solid Geometry

Rectangular coordinate systems in three dimensions

Direction cosines

Plane (straight line) and sphere
Mapping of CLOs to Program Learning Outcomes
CLO’s 
CLO1 (Fundamental Knowledge) 
CLO2 (Understand Application) 
CLO3 (Skill to Solve Problems) 
PLO’s 

PLO1 (Engineering Knowledge) 



PLO2 (Problem Analysis) 
√ 
√ 
√ 
PLO3 (Design/Development of Solutions) 



PLO4 (Investigation) 



PLO5 (Modern Tool Usage) 



PLO6 (The Engineer and Society) 



PLO7 (Environment and Sustainability) 



PLO8 (Ethics) 



PLO9 (Individual and Team work) 



PLO10 (Communication) 



PLO11 (Project Management) 



PLO12 (Lifelong Learning) 



Mapping of CLOs to Assessment Modules
CLOs 
CLO:1 
CLO:2 
CLO:3 
Assessment Modules 

Assignments (2025%) 
√ 
√ 

Quizzes (1520%) 
√ 
√ 

Midterm Exam (20%) 
√ 
√ 

Final Exam (4045%) 
√ 
√ 
√ 