I've been studying higher math on my own, and also at local colleges, and I spend a lot of time on Khan Academy (my profile is here). These pages show a proof of the work I've done. Update: 25 June 2015 (Completed Calculus III, Differential Equations, and Linear Algebra) From January to June 2015, I completed Calculus III during the Spring semester and Differential Equations and Linear Algebra during the Summer semester. I really wanted to get the math requirements behind me. Calculus II went well :) I found it very difficult and stressful but, I managed to pass now I'm moving on to Calculus III. Concepts I practiced are: Volumes Using CrossSections Volumes Using Cylindrical Shells Arc Length Areas of Surfaces of Revolution Work and Fluid Forces Moments and Centers of Mass The Logarithm Defined as an Integral Exponential Change and Separable Differential Equations Integration by Parts Trigonometric Integrals Trigonometric Substitutions Integration of Rational Functions by Partial Fractions Integral Tables and Computer Algebra Systems Improper Integrals Solutions, Slope Fields, and Euler's Method Indeterminate Forms and L'Hopital's Rule FirstOrder Linear Equations Sequences Infinite Series The Integral Test Comparison Tests The Ratio and Root Tests Alternating Series, Absolute and Conditional Convergence Power Series Taylor and Maclaurin Series Convergence of Taylor Series The Binomial Series and Applications of Taylor Series Polar Coordinates Graphing in Polar Coordinates Areas and Lengths in Polar Coordinates Vectors The Dot Product 22 August 2014 (Completed Sections 7.1 to 7.4 "Integration Techniques"  Calculus: Early Transcendental Functions by Roland Larson) Since this has been going so well, I decided to enroll in Calculus II at a local community college so I can get college credit for what I've learned. Being officially recognized as an aerospace engineering student has some advantages compared with going it alone (eg. access to internships), Section 7.4 was as far as I got before my class started. Concepts I practiced are: Basic Integration Rules Fitting Integrands to Basic Rules Integration by Parts Integrals Involving Powers of Sine and Cosine Integrals Involving Powers of Secant and Tangent Integrals Involving SineCosine Products with Different Angles Trigonometric Substitution 12 August 2014 (Completed Chapter 6 "Applications of Integration"  Calculus: Early Transcendental Functions by Roland Larson) Concepts I practiced are: Area of a Region Between Two Curves Area of a Region Between Intersecting Curves The Disc Method The Washer Method Solids with Known CrossSections The Shell Method Comparison of Disc and Shell Methods Arc Length Area of a Surface of Revolution Work Done by a Constant Force Work Done by a Variable Force Fluid Pressure and Fluid Force Mass Center of Mass in a OneDimensional System Center of Mass in a TwoDimensional System Center of Mass of a Planar Lamina 30 July 2014 (Completed Chapter 5 "Transcendental Functions & Differential Equations"  Calculus: Early Transcendental Functions by Roland Larson) Concepts I practiced are: Using the Log Rule Integrals of Trigonometric Functions Bases Other than e Differentiation and Integration Applications of Exponential Functions Differential Equations Growth & Decay Models General & Particular Solutions Separation of Variables Homogeneous Differential Equations Derivative of an Inverse Function Derivatives of Inverse Trigonometric Functions Review of Basic Differentiation Rules Integrals Involving Inverse Trigonometric Functions Completing the Square Review of Basic Integration Rules 22 July 2014 (Completed Chapter 4 "Integration"  Calculus: Early Transcendental Functions by Roland Larson) Since Khan Academy doesn't have their Integral Calculus course complete yet, I pulled out my old Calculus book from college. The last time I attempted to learn Calculus, learning Integration was what stopped me. Just really didn't get it and certainly couldn't apply it to anything. This time I was happy to note that it all made much more sense to me this time :) Concepts I practiced are: Antiderivatives Notation for antiderivatives Basic integration rules Initial conditions and particular solutions Sigma notation Area The area of a plane region Upper and lower sums Riemann sums Definite integrals properties of definite integrals The fundamental theorem of calculus The mean value theorem for integrals Average value of a function The second fundamental theorem of calculus Pattern recognition Change of variables The general power rule for integration Change of variables for definite integrals Integration of even and odd functions The natural logarithmic function The number e The natural logarithmic function and differentiation The Integral Calculus course on Khan Academy isn't quite fleshed out yet. Many parts are just videos. If a section only had videos, I skipped over it. Concepts I worked on are: Antiderivatives Using rectangles to approximate area under a curve, Area under a rate function equals net change, Evaluating definite integrals Functions defined by integrals The fundamental theorem of calculus 6 June 2014 (Completed the Differential Calculus course on Khan Academy)Integration by parts Integration by the reverse chain rule Integration by usubstitution Understanding sequences Geometric sequences Convergence and divergence of sequences Arithmetic series Understanding series Convergence and divergence of series Geometric series of constants Creating power series from geometric series using algebra Creating power series from geometric series using differentiation and integration Maclaurin series for sin x, cos x, and e^x
