Calculus I

Limits, derivatives and their applications to rates of change and optimization in engineering problems.

MATH-100 Year 1 3 credits 12 lessons · 8 h 50 min

Offered by HSM University · Engineering Core

What you'll learn

Evaluate limits, including indeterminate forms and limits at infinity, and decide where functions are continuous
Work with inverse, exponential, logarithmic and inverse trigonometric functions and use them to model growth, decay and logarithmic scales
Explain the derivative as a limit and as a rate of change, and use tangent lines and finite differences
Differentiate polynomial, trigonometric, exponential and composite functions, including implicitly
Differentiate inverse functions, use logarithmic differentiation, and interpret derivatives as rates in science and engineering
Apply the Mean Value Theorem and use first and second derivatives and asymptotes to sketch graphs
Solve related-rates and optimization problems, and apply Newton's method and L'Hôpital's rule
Find antiderivatives, solve initial value problems and simple differential equations, and apply Euler's method
Evaluate definite integrals with the Fundamental Theorem of Calculus and substitution, and apply them to net change, energy and average value
Compute areas between curves, RMS values and probabilities from density functions
Approximate functions with Taylor polynomials, bound their errors, and assess truncation and round-off error in numerical methods
Build, solve, check and communicate simple mathematical models of engineering systems

12 lessons · 8 h 50 min total · final exam

Limits, derivatives and their applications to rates of change and optimization in engineering problems.

Part of the Engineering stream, typically taken in year 1.