Master these skills and apply them to real-world projects.
Be able to apply techniques of calculus (learned in the first three semesters of a calculus sequence) to solve problems that arise in physics.
Derive and use the geometric series in calculations.
Manipulate power series expressions and employ them in physics contexts.
Calculate Taylor polynomials/series of common functions and use them in approximating functions
Follow the development for how one integrates polynomials, rational functions of polynomials, square roots of quadratics, rational functions with square roots of quadratics, and why the procedure cannot solve integrals with square roots of quartics.
Solve integrals via parametric methods (differentiating under the integral sign) including techniques for introducing the parameter into the integrand
Set up and integrate multidimensional integrals with variable mass density and for moments of inertia.
Solve problems in multivariable integrals via the different integral theorems
Solve Laplace's equation for simple geometries
Compute the curl or divergence of a vector field and the gradient of a scalar function
Solve complex numbers arithmetic problems
Use calculus of residues to solve integrals
Use row reduction to solve simultaneous linear equations
Calculate the determinant, inverse, and eigenvalues of matrices
Construct abstract vector spaces using the definitions of a vector space and generalized inner products
