There are two approaches that work well. The first is to embark on the standard, formative curriculum. The second is to start with a handful of problems that interest you and go pick up stuff piecemeal on the way to solving those.
Approach 1. Decide if you want to learn physics or applied mathematics. They're not the same. The math you describe is more on the operations research side of applied mathematics, and not terribly relevant to physics. You say your goals are physics. In that case you're in luck. The curriculum is utterly standard and consists of four passes through the material.
The first pass is one or two years long and is roughly what's in Halliday and Resnick or Tipler's physics books: Newtonian mechanics, some wave motion, some thermodynamics and statistical mechanics, electromagnetism, and a little "modern physics" (special relativity and a bit of quantum theory). Meanwhile you study calculus of a single variable, multivariable and vector calculus, and a little bit of ordinary differential equations, and do a year of laboratories.
The second pass is a semester of classical mechanics covering Lagrangian and Hamiltonian mechanics, a semester of statistical mechanics and thermodynamics, a year of electromagnetism, and a year of quantum mechanics, paired with a year of mathematical methods (linear algebra, special functions, curvilinear coordinates, a little tensor calculus, some linear partial differential equations, and a lot of Fourier analysis) and a year of more advanced laboratories. Here ends the undergraduate curriculum. At this point astrophysicists tend to separate off and start learning the knowledge for that domain instead of the second semesters of electromagnetism and quantum mechanics. Their labs are also different.
The third pass is the first couple years of graduate school, and goes through the same subjects again in more depth. No labs this time. A mathematical methods course only if a student needs more help. Quantum field theory for those going that direction. General relativity for those going another. Advanced statistical mechanics or other special topics for those going into condensed matter.
The fourth path is the student by themselves, integrating it all in preparation for doctoral qualifying exams.
If this approach sounds like what you're after, start by getting a 1960's edition of Halliday and Resnick's physics (which is better than the present editions and quite cheap used), a Schaum's outline of calculus.
Approach 2. Pick a handful of problems. What actually interests you? Not what sounds fascinating or what seems prestigious. What's interesting? Cloud shapes? Bird lifecycles? What are you actually curious enough about to spend some time poking at?
Approach 1. Decide if you want to learn physics or applied mathematics. They're not the same. The math you describe is more on the operations research side of applied mathematics, and not terribly relevant to physics. You say your goals are physics. In that case you're in luck. The curriculum is utterly standard and consists of four passes through the material.
The first pass is one or two years long and is roughly what's in Halliday and Resnick or Tipler's physics books: Newtonian mechanics, some wave motion, some thermodynamics and statistical mechanics, electromagnetism, and a little "modern physics" (special relativity and a bit of quantum theory). Meanwhile you study calculus of a single variable, multivariable and vector calculus, and a little bit of ordinary differential equations, and do a year of laboratories.
The second pass is a semester of classical mechanics covering Lagrangian and Hamiltonian mechanics, a semester of statistical mechanics and thermodynamics, a year of electromagnetism, and a year of quantum mechanics, paired with a year of mathematical methods (linear algebra, special functions, curvilinear coordinates, a little tensor calculus, some linear partial differential equations, and a lot of Fourier analysis) and a year of more advanced laboratories. Here ends the undergraduate curriculum. At this point astrophysicists tend to separate off and start learning the knowledge for that domain instead of the second semesters of electromagnetism and quantum mechanics. Their labs are also different.
The third pass is the first couple years of graduate school, and goes through the same subjects again in more depth. No labs this time. A mathematical methods course only if a student needs more help. Quantum field theory for those going that direction. General relativity for those going another. Advanced statistical mechanics or other special topics for those going into condensed matter.
The fourth path is the student by themselves, integrating it all in preparation for doctoral qualifying exams.
If this approach sounds like what you're after, start by getting a 1960's edition of Halliday and Resnick's physics (which is better than the present editions and quite cheap used), a Schaum's outline of calculus.
Approach 2. Pick a handful of problems. What actually interests you? Not what sounds fascinating or what seems prestigious. What's interesting? Cloud shapes? Bird lifecycles? What are you actually curious enough about to spend some time poking at?