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This uses both linear algebra and matrix by-product materials from Math fifty one. The unified treatment of each linear algebra and multivariable optimization is not coated in a single course accessible to non-majors anywhere else. Many college students who study some multivariable calculus earlier than arriving at Stanford discover Math 51 to be instructive to take as a outcome of its broad scope and synthesis of ideas.
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It is the primary course in the three part honors calculus sequence for school students majoring in arithmetic, science or engineering. Topics include limits, continuity, differentiation, functions of differentiation, and integration. Applications of the by-product are coated in detail, together with approximation of errors utilizing differentials, maxima and minima issues, curve sketching, optimization issues, and Newton’s technique. Topics on integration include Riemann sums, properties of definite integrals, integration by substitution and integrals involving logarithmic exponential and trigonometric functions.
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The course contains study of trigonometric features, inverse trigonometric features, trigonometric identities and trigonometric equations. Complex numbers, De Moivre’s Theorem, polar coordinates, vectors and different matters in algebra are also addressed, together with conic sections, sequences and collection. Its discrete math protection contains combinatorics, likelihood, some primary group concept, quantity principle, and graph principle. Students should have an interest in a theoretical method to the subject. Math 20- Calculus covers properties and purposes of integration, together with the Fundamental Theorem of Calculus and computations of volumes, areas, and arc size of parametric curves.