MATH1510 Calculus for Engineers
8/1/24
Does any resource help with this course?
What is this course about?
This course is an introduction to calculus for engineering students. The course covers the following topics:
- Vector Algebra and Functions
- vector algebra
- functions and their representations
- Limits and Continuity
- the limit of a function
- continuity
- limits involving infinity
- Derivatives
- derivatives and rate of changes
- differentiability
- derivative of trigonometric functions
- derivative of exponential functions & logarithmic functions
- implicit differentiation
- Polar and Inverse Trigonometric Functions
- polar coordinates
- inverse trigonometric functions
- Differentials and Higher Order Derivatives
- differentials
- derivatives and differentials of higher orders
- Graphs and Curve Sketching
- derivatives and the shapes of graphs
- curve sketching
- Theorems and Series
- the mean value theorem & Taylor/Maclaurin series
- indeterminate forms and L'Hopital's rule
- Antiderivatives and Integrals
- antiderivatives
- sigma notation, riemann sums and distances
- the definite integrals
- the fundamental theorem of calculus
- the substitution rule
- integration by parts
- trigonometric integrals and substitution
- Applications of Integrals
- applications of integrals: area between curves
- volume of a solid
- Partial Differentiations and Double Integrals
- partial differentiations
- double integrals
- Fourier Series
- applications of the fourier series
What is calculus?
Calculus is a branch of mathematics that deals with the study of rates of change. Calculus is divided into two main branches: differential calculus and integral calculus. Differential calculus deals with the study of rates of change, while integral calculus deals with the study of areas and volumes. Together, these two branches of calculus form the foundation of modern mathematics and science.