# Virtual University of Pakistan

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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

 Topic Lecture Resource Page Coordinates, Graphs, Lines 1 Handout 3-14 Absolute Value 2 Handout 15-23 Coordinate Planes and Graphs 3 Handout 24-33 Lines 4 Handout 34-44 Distance; Circles, Quadratic Equations 5 45-56 Functions 6 Handout 57-62 Operations on Functions 7 Handout 63-68 Graphing Functions 8 Handout 69-75 Limits (Intuitive Introduction 9 Handout 76-83 Limits (Computational Techniques) 10 Handout 84-92 Assignment No.1 Limits (Rigorous Approach) 11 Handout 93-96 Continuity 12 Handout 97-103 Limits and Continuity of Trigonometric Functions 13 Handout 104-109 Tangent Lines, Rates of Change 14 Handout 110-114 The Derivative 15 Handout 115-122 Quiz No. 1 Techniques of Differentiation 16 Handout 123-127 Derivatives of trigonometric functions 17 Handouts 128-131 The Chain Rule 18 Handout 132-135 Implicit Differentiation 19 Handout 136-138 Quiz No. 2 Derivatives of Inverse Functions 20 Handout 139-144 Applications of Differentiation. Relative Rates 21 Handout 145-150 Extreme Maxima 22 Handout 151-157 Midterm Exams Maximum and Minimum Values of Functions 23 Handout 158-163 Newton's Method, Roll's Theorem and the Mean Value Theorem 24 Handout 164-168 Integration 25 Handout 169-173 Integration by Substitution. 26 Handout 174-178 Sigma Notation 27 Handout 179-182 Area as Limit 28 Handout 183-190 Definite Integral 29 Handout 191-199 First Fundamental Theorem of Calculus 30 Handout 200-205 Assignment No. 2 Evaluating Definite Integral by Substitution 31 Handout 206-209 Second Fundamental Theorem of Calculus 32 Handout 210-213 Area between two curves 33 Handout 214-220 Volume by slicing; Disks and Washers 34 Handout 221-229 Volume by slicing; Disks and Washers 35 Handout 230-236 Length of Plane Curves 36 Handout 237-239 Quiz no.3 Area of Surface of Revolution 37 Handout 240-244 Work and Definite Integral 38 Handout 245-251 Improper Integral 39 Handout 252-257 L'Hopital's Rule 40 Handout 258-264 Sequence 41 Handout 265-275 Infinite Series 42 Handout 276-284 Additional Convergence tests 43 Handout 285-289 Alternating Series; Conditional Convergence 44 Handout 290-295 Taylor and Maclaurin Series 45 Handout 296-300 FINAL Exams