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Here are the topics covered in both classes:

Rigorous class

Topics to be covered include: Analysis - axioms for the real numbers, completeness, sequences and convergence, continuity, existence of extrema, limits, continuity, differentiation, inverse functions, transcendental functions, extrema, concavity and inflections, applications of derivatives, Taylor Polynomials, integration, differential equations; Linear Algebra - complex numbers, solving linear equations, matrix equations, linear independence, linear transformations, matrix operations, matrix inverses, subspaces, dimension and rank, determinants, Cramer's rule, volumes.

Non-rigorous class

Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions.Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Linear Algebra - Complex numbers. Solution of linear system of equations. Matrix algebra including matrix inverses, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Emphasis is on understanding and on using algorithms.