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MTH101 : Calculus And Analytical Geometry

Course Overview

Course Synopsis

Single variable calculus, which is what we begin with, can deal with motion of an object along a fixed path. The more general problem, when motion can take place on a surface, or in space, can be handled by multivariable calculus. So single variable calculus is the key to the general problem as well. The topics which will be covered in the course 'Calculus and Analytical Geometry MTH101' are Real numbers, set theory, intervals and inequalities, Lines, functions and graphs, Limits and Continuity, Differentiation, Integration and Sequence and Series. The study of calculus is normally aimed at giving you the "mathematical sophistication" to relate to such more advanced work. Calculus and Analytical Geometry MTH101 is pre-requisite course for Calculus II (MTH301).

Course Learning Outcomes

At the end of the course, you should be able to:

  • Use a variety of methods in solving real-life, practical, technical, and theoretical problems.
  • Select and use an appropriate problem-solving strategy.
  • Explain the limit process and that calculus centers around this concept.
  • Identify the two classical problems that were solved by the discovery of calculus, The tangent problem and the area problem.
  • Describe the two main branches of calculus, Differential calculus and Integral calculus.

Course Calendar

Coordinates, Graphs, Lines1Handout3-14
Absolute Value2Handout15-23
Coordinate Planes and Graphs3Handout24-33
Distance; Circles, Quadratic Equations545-56
Operations on Functions7Handout63-68
Graphing Functions8Handout69-75
Quiz No.1
Limits (Intuitive Introduction9Handout76-83
Limits (Computational Techniques)10Handout84-92
Limits (Rigorous Approach)11Handout93-96
Assignment No. 1
Limits and Continuity of Trigonometric Functions13Handout104-109
Tangent Lines, Rates of Change14Handout110-114
The Derivative15Handout115-122
Techniques of Differentiation16Handout123-127
Derivatives of trigonometric functions17Handouts128-131
The Chain Rule18Handout132-135
Implicit Differentiation19Handout136-138
GDB No. 1
Derivatives of Inverse Functions20Handout139-144
Applications of Differentiation. Relative Rates21Handout145-150
Extreme Maxima22Handout151-157
Midterm Exams
Maximum and Minimum Values of Functions23Handout158-163
Newton's Method, Roll's Theorem and the Mean Value Theorem24Handout164-168
Integration by Substitution.26Handout174-178
Sigma Notation27Handout179-182
Area as Limit28Handout183-190
Definite Integral29Handout191-199
First Fundamental Theorem of Calculus30Handout200-205
Assignment No. 2
Evaluating Definite Integral by Substitution31Handout206-209
Second Fundamental Theorem of Calculus32Handout210-213
Area between two curves33Handout214-220
Volume by slicing; Disks and Washers34Handout221-229
Volume by slicing; Disks and Washers35Handout230-236
GDB No. 2
Length of Plane Curves36Handout237-239
Area of Surface of Revolution37Handout240-244
Work and Definite Integral38Handout245-251
Improper Integral39Handout252-257
L'Hopital's Rule40Handout258-264
Quiz no.2
Infinite Series42Handout276-284
Additional Convergence tests43Handout285-289
Alternating Series; Conditional Convergence44Handout290-295
Taylor and Maclaurin Series45Handout296-300
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