Calculus & Linear Algebra for STEM
The calculus and linear algebra behind science, engineering and machine learning: derivatives, integrals, vectors, matrices, gradients and eigenvalues, with Python exercises.
Leads to: Data Scientist, Machine Learning Engineer, Civil Engineer, Mechanical Engineer, Electrical Engineer, Biochemist, Chemist, Physicist, Materials Scientist, Statistician, Actuary, Operations Research Analyst
Before you start
This course builds on Math for Tech & STEM. Take it first if you are new to the topic.
About this course
An intermediate course for learners who have finished Math for Tech & STEM. You will estimate and compute rates of change, use the derivative rules and optimise a design; treat integrals as accumulated area, integrate by substitution and simulate growth and decay with Euler's method; work with vectors, dot products, matrices and linear systems, and read a matrix as a transformation; and finish with partial derivatives, gradients, gradient descent and eigenvalues, plus a map of where these ideas appear in probability, machine learning, engineering and the physical sciences. Each lesson has a reading, free videos and a quiz, and most have a short Python exercise where the code already runs and you write the key line (some use NumPy).
Course content
Module 1
Derivatives
3 lessons · 2h 4mLimits, derivative rules and optimisation: how to measure and use rates of change, by hand and in code.
- 44mLimits and rates of changeReading
Go from the average rate of change between two points to the instantaneous rate at one point, and estimate it with code.
- 44mDerivative rulesReading
Differentiate polynomials, products and nested functions with the power, product and chain rules.
- 36mOptimisation with derivativesReading
Find the maximum or minimum of a quantity by setting its derivative to zero, by hand and numerically.
Module 2
Integrals
3 lessons · 2h 7mIntegrals as accumulated area, the fundamental theorem, substitution, and differential equations solved numerically.
- 44mArea and the integralReading
Treat the integral as accumulated area, approximate it with Riemann sums and connect it to derivatives.
- 31mIntegration techniquesReading
Use a table of antiderivatives and u-substitution to integrate functions that hide a chain rule.
- 52mIntro to differential equationsReading
Model growth and decay with dy/dt = ky, and simulate equations step by step with Euler's method.
Module 3
Vectors and Matrices
3 lessons · 2hVectors and dot products, matrices and linear systems, and matrices as transformations of space, with NumPy.
- 40mVectorsReading
Add and scale vectors, measure their length, and use the dot product to find angles and test for perpendicularity.
- 43mMatrices and systemsReading
Write a system of linear equations as A x = b, multiply matrices, and solve the system with NumPy.
- 37mLinear transformationsReading
Read a matrix as a transformation of space: rotations, scalings and shears, composition, and the determinant as area scale.
Module 4
Multivariable Ideas
3 lessons · 1h 37mPartial derivatives, gradients and eigenvalues, and how all of this course powers probability, machine learning and engineering.
- 31mPartial derivatives and gradientsReading
Take derivatives of functions of several variables, build the gradient, and use it for gradient descent.
- 36mEigenvaluesReading
Find the vectors a matrix only stretches, compute eigenvalues by hand and by power iteration, and see where they matter.
- 30mWhere this shows upReading
Connect derivatives, integrals, gradients and matrices to probability, machine learning, engineering and science.