Many students who learn some multivariable calculus before arriving at Stanford find Math 51 to be instructive to take due to its broad scope and synthesis of concepts. The unified treatment of both linear algebra (beyond dimension 3 and including eigenvalues) and multivariable optimization is not covered in a single course accessible to non-majors anywhere else. This material includes the basic geometry and algebra of vectors, matrices, and linear transformations, as well as optimization techniques in any number of variables (involving partial derivatives and Lagrange multipliers). Math 51- Linear Algebra, Multivariable Calculus, and Modern Applications (5 units) covers linear algebra and multivariable differential calculus in a unified manner alongside applications related to many quantitative fields. The department offers 3 sequences in multivariable mathematics. If you took multivariable calculus elsewhere, please click the button below:Īlready took some multivariable calculus? Knowledge of Math 21 content is fundamental to university-level quantitative work, and is expected by the outside world for anyone earning a degree in a quantitative field here. This is an enforced requirement to enroll in Math 51 or CME 100 for more details, click on the red button above. The math placement diagnostic results do not waive Math 21 requirements, since the diagnostic has no exam security its feedback is purely advisory. The content of Math 21 (improper integrals, infinite series, and power series) is essentially the material of BC-level AP calculus not in the syllabus of AB-level AP calculus nor in IB Higher Level math. ![]() Taylor series and applications are also covered. Math 21- Calculus (4 units) covers limits at infinity and unbounded functions in the context of integration as well as infinite sums, including convergence/divergence tests and power series. An introduction to some basic notions related to differential equations (such as exponential growth/decay and separable equations) is also given. ![]() Math 20- Calculus (3 units) covers properties and applications of integration, including the Fundamental Theorem of Calculus and computations of volumes, areas, and arc length of parametric curves. ![]() Calculations involve trigonometric functions, exponentials, and logarithms, and applications include max/min problems and curve-sketching. Math 19- Calculus (3 units) covers properties and applications of limits, continuous functions, and derivatives. It can be started at any point in the sequence for those with sufficient background. This series covers differential calculus, integral calculus, and power series in one variable.
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