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General Science · Year 1 · Foundations
S2 Calculus, linear algebra and mechanics
Master differential and integral calculus and linear algebra, then apply them to Newtonian mechanics; broaden biology to ecology and evolution.
226hours of coursework
23weeks at 10 h
5steps
17new courses
2universities
Target skills
- Limits, derivatives, differentiation rules and optimisation
- Integrals, series, integration techniques, introduction to vector calculus
- Linear systems, matrices, determinants, eigenvalues, orthogonality
- Kinematics, forces, energy, momentum, rotation and gravitation
- Ecology, evolution and biodiversity
Semester project
Simulate in Python the trajectory of a projectile with air drag using Euler's method, compare it with the drag-free solution and plot both curves.
Courses this semester
- 1Johns Hopkins UniversityIntermediateData Analysis Software
Stated prerequisites: Some familiarity with precalculus, specifically exponential and logarithm functions
Show the 4 courses
Course Level Length Rating (reviews) Calculus through Data & Modeling: Precalculus Review Beginner 8 h 4.8 (124) Calculus through Data & Modeling: Limits & Derivatives Beginner 10 h 4.7 (212) Calculus through Data & Modeling: Differentiation Rules Intermediate 8 h 4.8 (124) Calculus through Data & Modeling: Applying Differentiation Intermediate 7 h 4.7 (63) - 2Johns Hopkins UniversityIntermediate
Stated prerequisites: Working knowledge of differential calculus
Show the 4 courses
Course Level Length Rating (reviews) Calculus through Data & Modelling: Series and Integration Intermediate 9 h 4.9 (63) Calculus through Data & Modelling: Techniques of Integration Intermediate 5 h 4.7 (55) Calculus through Data & Modelling: Integration Applications Intermediate 6 h 4.6 (28) Calculus through Data & Modelling: Vector Calculus Intermediate 5 h 4.7 (53) - 3Johns Hopkins UniversityBeginner
Stated prerequisites: Basic algebra (no calculus)
Show the 3 courses
Course Level Length Rating (reviews) Linear Algebra: Linear Systems and Matrix Equations Beginner 10 h 4.7 (183) Linear Algebra: Matrix Algebra, Determinants, & Eigenvectors — 15 h 4.8 (79) Linear Algebra: Orthogonality and Diagonalization Intermediate 9 h 4.8 (56) - 4Rice UniversityIntermediate
Stated prerequisites: Algebra, geometry, trigonometry; basic calculus helpful
Show the 3 courses
Course Level Length Rating (reviews) Physics 101 - Forces and Kinematics Intermediate 30 h 4.7 (210) Physics 101 - Energy and Momentum Intermediate 23 h 4.6 (49) Physics 101 - Rotational Motion and Gravitation Intermediate 28 h 4.8 (104) - 5Rice UniversityBeginner
Show the 3 courses
Course Level Length Rating (reviews) Introduction to Biology: Ecology Beginner 18 h 4.8 (184) Introduction to Biology: Evolution Beginner 12 h 4.9 (91) Introduction to Biology: Biodiversity Beginner 23 h 4.8 (84)
Reading
Calculus, Volumes 1 to 3OpenStaxVolume 1 for differentiation, Volume 2 for integration and series.Free, CC BY 4.0
Linear AlgebraJim HefferonA complete textbook with worked exercises, alongside the Johns Hopkins specialization.Free
University Physics, Volumes 1 to 3OpenStaxUniversity-level mechanics, chapters 1 to 13, alongside Rice.Free, CC BY 4.0
The Feynman Lectures on PhysicsR. P. Feynman, R. B. Leighton, M. SandsThe mechanics chapters, to understand the ideas behind the equations.Free to read online
Things to watch
- Take Differential Calculus before Integral Calculus, then Linear Algebra.
- Introduction to Mechanics belongs in the second half of the semester, once derivatives are mastered.
With Coursera Plus
This semester takes 226 hours, about 5 months at 10 hours a week. A Coursera Plus subscription gives access to most of its courses during that time.