Basic Mathematics
Course Code: MTH104 Pass Marks: 32 (Theory) + 8 (Internal)
Nature of Course: Theory
Credit Hours: 3
Course Description
This course helps students understand the basic concepts of mathematics used in science and technology. It focuses on functions, limits, continuity, differentiation, integration, differential equations, and partial derivatives. The course also explains how mathematics can be used to solve real-life problems.
Course Objectives
Unit 1: Functions and Graphs (5 Hours)
This unit introduces functions and their graphs. Students learn how to combine functions and change graphs by shifting or scaling them. It also includes trigonometric functions, exponential and logarithmic functions, inverse functions, and the idea of rate of change and tangents to curves.
Credit Hours: 3
Course Description
This course helps students understand the basic concepts of mathematics used in science and technology. It focuses on functions, limits, continuity, differentiation, integration, differential equations, and partial derivatives. The course also explains how mathematics can be used to solve real-life problems.
Course Objectives
- After completing this course, students will be able to:
- Understand real-world problems and express them using mathematical language.
- Solve mathematical problems at a level suitable for this course.
- Explain mathematical solutions using numbers, formulas, graphs, or diagrams.
Unit 1: Functions and Graphs (5 Hours)
This unit introduces functions and their graphs. Students learn how to combine functions and change graphs by shifting or scaling them. It also includes trigonometric functions, exponential and logarithmic functions, inverse functions, and the idea of rate of change and tangents to curves.
Unit 2: Limits and Continuity (3 Hours)
This unit explains the concept of limits and how they are calculated. It covers limit laws, one-sided limits, continuity of functions, limits involving infinity, and asymptotes of graphs.
This unit explains the concept of limits and how they are calculated. It covers limit laws, one-sided limits, continuity of functions, limits involving infinity, and asymptotes of graphs.
Unit 3: Differentiation (5 Hours)
In this unit, students learn about derivatives and how to calculate them. Topics include tangents, derivatives as rates of change, derivatives of trigonometric functions, the chain rule, implicit differentiation, inverse functions, logarithmic functions, and related rates.
In this unit, students learn about derivatives and how to calculate them. Topics include tangents, derivatives as rates of change, derivatives of trigonometric functions, the chain rule, implicit differentiation, inverse functions, logarithmic functions, and related rates.
Unit 4: Applications of Derivatives (5 Hours)
This unit shows how derivatives are used in practical problems. It includes finding maximum and minimum values, mean value theorem, increasing and decreasing functions, curve sketching, L’Hôpital’s rule, optimization problems, and Newton’s method.
This unit shows how derivatives are used in practical problems. It includes finding maximum and minimum values, mean value theorem, increasing and decreasing functions, curve sketching, L’Hôpital’s rule, optimization problems, and Newton’s method.
Unit 5: Integration (5 Hours)
This unit introduces integration and antiderivatives. Students learn about area under curves, definite and indefinite integrals, the fundamental theorem of calculus, substitution method, and finding the area between curves.
This unit introduces integration and antiderivatives. Students learn about area under curves, definite and indefinite integrals, the fundamental theorem of calculus, substitution method, and finding the area between curves.
Unit 6: Applications of Definite Integrals (3 Hours)
This unit explains how definite integrals are used to find volumes, arc lengths, surface areas, work done, fluid forces, moments, and centers of mass.
This unit explains how definite integrals are used to find volumes, arc lengths, surface areas, work done, fluid forces, moments, and centers of mass.
Unit 7: Techniques of Integration (5 Hours)
This unit focuses on different methods of integration. Topics include integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, numerical integration, improper integrals, and the use of calculators and computer software.
This unit focuses on different methods of integration. Topics include integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, numerical integration, improper integrals, and the use of calculators and computer software.
Unit 8: First-Order Differential Equations (4 Hours)
This unit introduces basic differential equations and their solutions. It includes slope fields, Euler’s method, linear equations, applications, graphical solutions, systems of equations, and phase planes.
This unit introduces basic differential equations and their solutions. It includes slope fields, Euler’s method, linear equations, applications, graphical solutions, systems of equations, and phase planes.
Unit 9: Infinite Sequences and Series (5 Hours)
This unit explains sequences and infinite series. Topics include convergence tests, alternating series, power series, Taylor and Maclaurin series, and understanding when a series converges or diverges.
This unit explains sequences and infinite series. Topics include convergence tests, alternating series, power series, Taylor and Maclaurin series, and understanding when a series converges or diverges.
Unit 10: Partial Derivatives (5 Hours)
This unit introduces functions of more than one variable. Students learn about limits and continuity in higher dimensions, partial derivatives, chain rule, gradients, tangent planes, maximum and minimum values, Lagrange multipliers, and Taylor’s formula for two variables.
This unit introduces functions of more than one variable. Students learn about limits and continuity in higher dimensions, partial derivatives, chain rule, gradients, tangent planes, maximum and minimum values, Lagrange multipliers, and Taylor’s formula for two variables.
Text / Reference Book
Maurice D. Weir and Joel Hass, Thomas’ Calculus: Early Transcendentals, 12th Edition, 2009
Maurice D. Weir and Joel Hass, Thomas’ Calculus: Early Transcendentals, 12th Edition, 2009
