Around here, Calc I is a 1st semester class in an engineering program and that assumes you have the equivalent knowledge of Pre-Calc which is a two semester class. Pre-Calc assumes a decent background from high school. But 2 semesters is a full year and it doesn't even count toward graduation. That's one of the reasons engineering programs are now more typically 5 years than 4. And don't even think about skipping Pre-Calc, you will struggle mightily with the low level details when you take Calc I. There is a saying that "Calculus is easy, it's Pre-Calc that's difficult!". It's a fair assessment. Here's a hint: Don't take Pre-Calc I as a short summer class.
Given the Internet and resources like Khan Academy and CalcWorkshop (fee), math is getting more approachable. There are so many tutorials just watch some and see how it works out. NancyPi is good (and easy on the eyes). Her channel used to be MathBff.
One comment......
Methods of solving definite integrals of rational expressions using Partial Fractions Decomposition. The one often poorly covered topic from Precalc1 that comes back to rape you in Calc2.
How interesting you should bring that up! Everybody should have to know that method and actually be able to use it and do just one problem! The rest of the time they would be better served to use MATLAB. It knows more about factoring and partial fractions than I'll ever know.
Last weekend, my grandson and I were working on a problem for his MATLAB class - a required course in the engineering curriculum. It has to do with the shift in the color of an object as it approaches the speed of light known as the relativistic Doppler shift. He had not been taught to use the solve() function (it's just the first week) so he had to do all the algebra to solve the ugly equation in terms of v and then let MATLAB just plug in the numbers. But MATLAB knows more about algebra than we will ever. Use the solve() function and leave it alone.
The equation:
lp = ls * sqrt( (1-v/c) / (1+v/c) )
v is the velocity at which the color has changed and c is the speed of light.
It's really kind of ugly dividing both sides by ls, squaring both sides and then clearing out that fraction. Or you can use MATLAB solve()
[font=courier]
syms v % approach velocity at which red light appears green
c = 300e6; % speed of light in meters/second
ls = 630; % wavelength of red light
lp = 530; % wavelength of green light
eq1 = lp == ls * sqrt((1-(v/c))/(1+(v/c)));
vel = solve(eq1,v); % solve for v and put result in vel
format shortEng % exponents are multiples of 3
double(vel) % print result as numeric doouble precision
ans =
51.3426e+006
[/font]
So, at about 51,000,000 meters per second (or just 51,000 km/second) which is about 0.6 times the speed of light, a red light will appear green.
Obviously, MATLAB can do things like definite and indefinite integrals, take derivatives, mess around with trigonometric functions and a whole lot more. I'm not a salesman but I am a huge fan.
>> syms x
>> int( sin(x) ) % indefinite integral of sin(x)
ans =
-cos(x)
Octave is free and will do the same kinds of things. I think a first semester course in MATLAB is definitely the way to go.