Calculus and Analytical Geometry (MTCE1013)

Pre-requisite(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 co-ordinate systems in three dimensions

  • Direction cosines

  • Plane (straight line) and sphere

Mapping of CLOs to Program Learning Outcomes

CLO’s

CLO-1

(Fundamental  Knowledge)

CLO-2

 (Understand Application)

CLO-3

 (Skill to Solve Problems)

PLO’s

PLO-1

(Engineering Knowledge)

 

 

 

PLO-2

(Problem Analysis)

PLO-3

(Design/Development of Solutions)

 

 

 

PLO-4

(Investigation)

 

 

 

PLO-5

(Modern Tool Usage)

 

 

 

PLO-6

(The Engineer and Society)

 

 

 

PLO-7

(Environment and Sustainability)

 

 

 

PLO-8

(Ethics)

 

 

 

PLO-9

(Individual and Team work)

 

 

 

PLO-10

(Communication)

 

 

 

PLO-11

(Project Management)

 

 

 

PLO-12

(Lifelong Learning)

 

 

 

Mapping of CLOs to Assessment Modules

CLOs

CLO:1

CLO:2

CLO:3

Assessment Modules

Assignments (20-25%)

 

Quizzes (15-20%)

 

Midterm Exam (20%)

 

Final Exam (40-45%)