Basic Engineering Mathematics
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Basic Engineering Mathematics
This course is part of Mathematics for Engineering Specialization
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What you'll learn
Integrate trigonometric concepts to analyse and solve complex real-world engineering problems.
Critically evaluate and solve intricate systems of linear equations using matrix operations.
Synthesise the principles of differentiation and integration to develop and optimise engineering models.
Formulate and solve first-order and first-degree differential equations to effectively model a variety of engineering processes.
Details to know
22 assignments
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There are 6 modules in this course
Master the fundamental mathematical principles critical for engineering success with our Comprehensive Engineering Mathematics course. This structured program builds your proficiency in complex numbers, matrices, trigonometry, and calculusβthe essential mathematical toolkit for any engineer. Through practical examples and real-world applications, you'll develop the analytical skills necessary to solve engineering problems across various disciplines. The course progresses logically from algebraic concepts to advanced calculus techniques, ensuring a solid foundation for further engineering studies. By completion, you'll confidently apply these mathematical tools to model, analyze, and solve engineering challenges in your professional work or academic pursuits.
Skills Covered - Complex Number Operations and Applications - Matrix Algebra and System Solutions - Trigonometric Function Analysis - Differential Calculus Techniques - Integral Calculus Applications - Differential Equation Modeling - Mathematical Problem-Solving for Engineering
Explore real and complex number systems, operations in the Argand plane, and techniques for solving quadratic equations using factorization and formula methods.
What's included
11 videos3 readings4 assignments
11 videosβ’Total 64 minutes
- Basic Mathematicsβ’2 minutes
- Real & complex number systemβ’4 minutes
- Argand Planeβ’5 minutes
- Complex conjugateβ’8 minutes
- Algebra of complex numbersβ’9 minutes
- Algebra of complex numbers - Examplesβ’7 minutes
- Types of equationsβ’7 minutes
- Roots of a quadratic equation by factorizationβ’8 minutes
- Roots of a quadratic equation by the formulaβ’4 minutes
- Roots of a quadratic equation - Examplesβ’5 minutes
- Quadratic equation & rootsβ’5 minutes
3 readingsβ’Total 25 minutes
- Course Overview & Informationβ’10 minutes
- Recommended Reading: Complex Numbers & Quadratic Equationsβ’5 minutes
- Summary: Complex Numbers & Quadratic Equationsβ’10 minutes
4 assignmentsβ’Total 90 minutes
- Test Yourself: Complex Numbers & Quadratic Equationsβ’30 minutes
- Check Your Understanding: Complex Numbersβ’15 minutes
- Check Your Understanding: Quadratic Equationsβ’15 minutes
- Copy of Check Your Understanding: Quadratic Equationsβ’30 minutes
Master matrix operations, types, inverse calculations, solving systems of equations, and determining matrix rank for engineering applications.
What's included
12 videos4 readings5 assignments
12 videosβ’Total 94 minutes
- Definition of a matrixβ’6 minutes
- Types of matricesβ’11 minutes
- Algebraic operations on matricesβ’9 minutes
- Algebra of matrices β Examplesβ’10 minutes
- Inverse of a matrix by ad joint methodβ’9 minutes
- Inverse of a matrix β Example 1β’6 minutes
- System of equations - Introductionβ’9 minutes
- System of equations β Matrix formβ’7 minutes
- Solution of system of equationsβ’5 minutes
- Solution of system of equations - Examplesβ’5 minutes
- Rank of a matrixβ’10 minutes
- Rank of a matrix - Examplesβ’6 minutes
4 readingsβ’Total 25 minutes
- Recommended Reading: Matricesβ’5 minutes
- Recommended Reading: Inverse of a Matrix & System of Equationsβ’5 minutes
- Recommended Reading: Rank of a matrix and its propertiesβ’5 minutes
- Summary: Matricesβ’10 minutes
5 assignmentsβ’Total 78 minutes
- Test Yourself: Matricesβ’30 minutes
- Check Your Understanding: Algebra of Matricesβ’15 minutes
- Check Your Understanding: Inverse of a Matrixβ’9 minutes
- Check Your Understanding: System of Equationsβ’15 minutes
- Check Your Understanding: Rank of a matrixβ’9 minutes
Develop proficiency in trigonometric relationships, identities, and practical applications in engineering problems.
What's included
8 videos3 readings3 assignments
8 videosβ’Total 38 minutes
- Basics of Trigonometryβ’4 minutes
- Trigonometric Relationsβ’8 minutes
- Basics of Trigonometry: Examplesβ’3 minutes
- Trigonometric Identitiesβ’5 minutes
- Trigonometric Identities - Example 1β’4 minutes
- Trigonometric Identities - Example 2β’6 minutes
- Applications of Trigonometry - 1β’3 minutes
- Applications of Trigonometry - 2β’5 minutes
3 readingsβ’Total 20 minutes
- Recommended Reading: Trigonometryβ’5 minutes
- Recommended Reading: Applications of Trigonometryβ’5 minutes
- Summary: Trigonometryβ’10 minutes
3 assignmentsβ’Total 57 minutes
- Test Yourself: Trigonometryβ’30 minutes
- Check Your Understanding: Trigonometryβ’15 minutes
- Check Your Understanding: Applications of Trigonometryβ’12 minutes
Learn about functions, limits, continuity, differentiation techniques, and applications including optimization and the mean value theorem.
What's included
17 videos2 readings4 assignments
17 videosβ’Total 151 minutes
- Functionsβ’6 minutes
- Types of functionsβ’11 minutes
- Definition of Limitβ’8 minutes
- Standard form, standard limitsβ’11 minutes
- Indeterminate formsβ’9 minutes
- Limits - Examplesβ’10 minutes
- Continuity Definitionβ’10 minutes
- Continuity - Examplesβ’9 minutes
- Differentiabilityβ’6 minutes
- Derivative of standard functionsβ’9 minutes
- Derivative of standard functions - Exampleβ’6 minutes
- Derivatives - Propertiesβ’8 minutes
- Mean Value Theoremβ’9 minutes
- Applications of Derivatives - Examplesβ’9 minutes
- Applications of Derivatives - Maximum and Minimum of a Functionβ’9 minutes
- Applications of Derivatives β First Derivative Testβ’11 minutes
- Applications of Derivatives β Second Derivative Testβ’11 minutes
2 readingsβ’Total 15 minutes
- Recommended Reading: Relations and Functions, Limits and Derivatives, Continuity and Differentiabilityβ’5 minutes
- Summary: Differential Calculus and its Applicationsβ’10 minutes
4 assignmentsβ’Total 75 minutes
- Test Yourself: Differential Calculus and its Applicationsβ’30 minutes
- Check Your Understanding: Limits and Continuityβ’15 minutes
- Check Your Understanding: Differentiationβ’15 minutes
- Check Your Understanding: Applications of Derivativesβ’15 minutes
Study integration methods, standard functions, properties, product rule, and applications to engineering problems.
What's included
8 videos1 reading3 assignments
8 videosβ’Total 64 minutes
- Integral of a functionβ’7 minutes
- Propertiesβ’5 minutes
- Methods of Integration - 1β’9 minutes
- Methods of Integration - 2β’7 minutes
- Product Ruleβ’8 minutes
- Definite integralsβ’12 minutes
- Applications of Integration β Examplesβ’8 minutes
- Applications of Integration - Examplesβ’8 minutes
1 readingβ’Total 10 minutes
- Summary: Integral Calculus and its Applicationsβ’10 minutes
3 assignmentsβ’Total 57 minutes
- Test Yourself: Integral Calculus and its Applicationsβ’30 minutes
- Check Your Understanding: Integrationβ’15 minutes
- Check Your Understanding: Applications of Integrationβ’12 minutes
Understand differential equation types, order, degree, and solution methods for first-order equations including variable separable, homogeneous, and linear forms.
What's included
7 videos2 readings3 assignments
7 videosβ’Total 62 minutes
- Types of Differential Equationsβ’6 minutes
- Order and Degree of a Differential Equationβ’6 minutes
- First Order and First Degree Differential Equations β Variables Separableβ’8 minutes
- Homogeneous Differential Equationsβ’10 minutes
- Non-homogeneous Differential Equationsβ’9 minutes
- Exact and Nonβexact Differential Equationβ’14 minutes
- First Order Linear Differential Equationsβ’9 minutes
2 readingsβ’Total 20 minutes
- Summary: Ordinary Differential Equationsβ’10 minutes
- Course Summaryβ’10 minutes
3 assignmentsβ’Total 57 minutes
- Test Yourself: Ordinary Differential Equationsβ’30 minutes
- Check Your Understanding: Types of Differential Equationsβ’12 minutes
- Check Your Understanding: First Order and First Degree Differential Equationsβ’15 minutes
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Taking this course by Birla Institute of Technology & Science, Pilani may provide you with a preview of the topics, materials and instructors in a related degree program which can help you decide if the topic or university is right for you.
Instructor
Explore more from Math and Logic
- Status: Free TrialB
Birla Institute of Technology & Science, Pilani
Specialization
- Status: PreviewK
Korea Advanced Institute of Science and Technology(KAIST)
Course
- Status: PreviewK
Korea Advanced Institute of Science and Technology(KAIST)
Course
- Status: Free TrialT
The Hong Kong University of Science and Technology
Course
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Reviewed on Jul 23, 2025
The course overall is very good, however I think the last parts (integration and differential equations) could be made much clearer
Reviewed on Apr 8, 2025
a very good course for basic mathematics by BITS Pilani institute
Reviewed on Dec 29, 2024
This is a good refresher for anyone who is starting with or brushing up basic math
Frequently asked questions
This course covers fundamental mathematics concepts essential for engineering disciplines. It's important because these mathematical tools form the foundation of engineering analysis, modeling, and problem-solving across all engineering fields.
This course is designed for engineering students, technical professionals seeking to refresh their skills, and anyone needing a solid foundation in engineering mathematics for academic or professional advancement.
You'll be able to solve problems involving complex numbers, matrices, trigonometric functions, derivatives, integrals, and differential equations. These skills will enable you to tackle a wide range of engineering problems that require mathematical modeling and analysis.
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