MAT 104: Calculus and Analytical Geometry

Description

This is one of the foundation courses offered by the university, which fulfills the requirement of foundation in “Numeracy”. This course is mandatory for the students who wish to major in Computer Science and Engineering.

Topics include: Functions and their visualization, limits, and continuity; Differential calculus, differentiation of product and quotient; Successive differentiation. Additional techniques of integration. Interpretations of the derivative, applications of the derivative to geometry, mechanics, marginality and optimization. Newton’s method. Introduction to modeling; Integral calculus, integration by parts; Definite integral, interpretations and properties of the definite integral, applications of the definite integral to geometry, mechanics, economics and modeling. Approximating definite integral, approximation errors and Simpson’s rule, improper integrals. Taylor polynomials and series, convergence of series, finding and using Taylor’s series, indeterminate forms, Fourier series. First order differential equations: Slope fields, Euler’s method, separation of variables, linear equations, applications and modeling.

Website for the Department of Physical Sciences - http://www.secs.iub.edu.bd/PHYS/index.php

Prerequisites:
• None

Course Type Foundation 3 45
Expected Outcome(s):
• Define, graph, compute limits of, differentiate, and integrate transcendental functions.
• Examine various techniques of integration and apply them to definite and improper integrals.
• Approximate definite integrals using numerical integration techniques and solve related problems.
• Model physical phenomena using differential equations.
• Define, graph, compute limits of, differentiate, integrate and solve related problems involving functions represented parametrically or in polar coordinates.
• Distinguish between the concepts of sequence and series, and determine limits of sequences and convergence and approximate sums of series.
• Define, differentiate, and integrate functions represented using power series expansions, including Taylor series, and solve related problems.

2 Class Tests, One Midterm Exam, One Final Exam